[I'm not a writer, I'm mostly a reader, but I thought I'd give my impressions as I read this. The other anon's advice probably comes from actually being able to write, so I'd follow that too.
I've put my own additions inside [] brackets. Hopefully it's legible.]

Anon ran as fast as he could, as though any hesitation would result in his death. For all he knew it very well could. Ducking in and out of alleyways after checking if the building [Only one single building?] in front of him had left its doors unlocked. [A building doesn't lock or unlock its own doors, which the phrasing suggests. "Had had its doors left unlocked", for example.]  While he was willing to break a window, that would cause questions in the morning, and possibly attract attention to him. He was like an animal: scared, desperate, and hungry. That was not lost on him, but he would have time to loath[e - "loath" is an adjective] himself and his circumstances later when he wasn't so hungry. Maybe if he was lucky he could find out where in Equestria he had woken up in ["where in Equestria in"].

Anon had gone to sleep same as any night. Halfheartedly browsing /mlp/ as music lulled him towards unconsciousness [This sentence is a stub - either join it with a previous one with e.g.  a colon (though that's not recommended especially for newer writers), or add a subject: "He'd been healfheartedly browsing..."]. He hated laying in bed waiting for sleep to come. He always needed some form of entertainment to make the transitory period less grating. He tried to retrace his steps, yet there was nothing out of the ordinary. He was melancholic that night, and sleep did not come easy, but it did come, or so he thought. When he first woke up next to a pile of trash in some alleyway, his first thought was that he was either dreaming, or that he was somehow burglarized, kidnapped, drugged and left there. Yet neither seemed particularly likely. [This paragraph is kinda dry in the middle: "He hated X. He always X. He did X. He was X, or so he thought. When He woke up, X." - could be worth varying it up a bit.]
Impossible was a far more apt description, but it still happened. The city was not one he recognized. He still had his clothes, so there was some small silver lining at least. Yet as he lifted himself off the ground, his heart felt as though it would burst from his chest, it was beating so fast. Ponies, walking the streets. After seeing them, he needed no help returning to the ground. He practically collapsed. The world seemed to spin, but there was no indication Anon was being sent back to his own world. What could have caused this? Why? A million questions raced through his mind. The world kept moving without him. Equestrians went about their days none the wiser to the alien in the alleyway about to suffer a heart attack. [This paragraph reads better, but a couple of really short sentences are a bit out of place. Sentence length gives a lot of the tone - a short sentence is like a highlight, and can be used in succession to instill urgency (e.g. something like "He ran. They were behind him. He glanced back - they were gaining.") or drop something particularly important (e.g. in this case, works well for "The city was not one he recognised." - this is a key piece of information, it's surprising and unusual and very important to the plot, so it's good to keep it short and just let the sentence stand there - let the reader process it). But then, after this revelation, you launch into a description of Anon having a breakdown/heart attack, and there aren't any more bombshells to drop like that - that "He practically collapsed" is not some kind of surprise when you implied that in just the previous sentence, and "The world kept moving without him" is a very mundane and expected thing. For the latter, even simply adding a "But" at the beginning of the sentence would help to frame why you're saying that at all.]

Minutes turned to hours, but he did not leave his cover. He couldn't leave. What would the ponies do if they found him? "If an alien landed on earth, it would probably get shot or dissected. Maybe both." [Add some attribution - those are anon's thoughts, yes? It's clear if you think about it but it's not obvious at a glance (maybe some pony approached him and started talking) and breaks the flow of reading.] Yet Equestria was a far different place than Earth. Anon knew that as well as anyone, but a positive response was not something he was willing to risk. As he calmed down, a plan began to piece together in his mind.

"If this is Equestria, there are alicorns with enough power to get me back home. I just have to find them."
Yet that would be easier said than done. Surely Celestia and Luna's guards wouldn't let some alien creature speak with them just because he asked. Same with Cadence. But Twilight went around Ponyville unguarded all the time. All he had to do was get there. The plan sounded crazy. [Again, the previous sentence is good, but this sentence is too short for no reason - merging it with the next one should help the flow flow better, if you'll forgive the word choice.] It was, but it was all he had. For once he didn't think about how dreadful it would be to talk to someone, let alone Twilight Sparkle of all people. He only thought of carrying it out.

Yet as he seemed to fully calm down, [Normally those rules are stupid but still, starting a paragraph with "yet" can feel awkward unless you have a good reason.] the sun had already set, and the activity in the streets seemed to thin. The entire day not one pony [had] noticed him. Probably for the best. [Too short sentence] Wherever he was, he could stow away on a train to Ponyville. It couldn't be that hard. Hobos did stuff like that all the time, minus the Ponyville part, of course. [See, you didn't split that into multiple sentences. Though, mind, I'm not saying you should replace periods with commas everywhere and call it a day, that would also quickly lead to poor structure and flow.] The growling of his stomach reminded him of the human element he had forgotten to take into account. He needed food and water, or he'd die. As sure as he was of his master plan, when he was forced to leave his spot to find food, a wave of uncertainty washed over him. Even so, he wasn't willing to eat garbage just yet.  It [the city wasn't mentioned previously, so "it" can't really refer to it (hey, see, here it can, since I started the sentence talking about it) - "This wasn't a city..." would work well instead. Or "He wasn't in a city...", for example.] wasn't a city he recognized from the show. Smaller than Manehattan, but certainly not Canterlot.

The Vanhoover Star [In actual prose, you'd have to give this some description and framing, e.g.: "He read a sign hanging across the street: 'The Vanhoover Star'. Vanhoover?" etc.]

Vanhoover? That's where he was. No wonder he didn't recognize much. It wasn't too far by train from Ponyville, right? Anon had never ridden a train before, so how long it would take. [What is this trainwreck of a phrase? "...so he wasn't sure how long it would take." Don't get too fancy, but don't forget to use your words.] Still[,] that all was secondary to finding something to eat. He tried the door, and for once it opened. "Eat shit, suckers!" [Again, some framing - I'm not actually sure if this is still internal monologue or if he just exclaimed that out loud. Also, this remark seems really out of place - one moment he was super serious mode, recovering from an existential crisis and figuring out how not to die, and now suddenly this?] If this was a newspaper building, it couldn't be unlike any other office. If that were the case, ["If X, Y. If so, Z." - vary things up a bit. E.g. ", and that meant at least a few people..."] at least a few people had to keep food here. For the first time since waking up Anon felt his luck turning around. He could stock up on food here, and scout out the train yard. [Then] He'd be off to see Twilight [that "then" helps connect the sentences and give some context - that's his plan. He was already planning to visit Twilight in general previously (he didn't just decide he would), so just saying that he'd be off to see her doesn't mean much; what's important is that he's decided it's going to be what he does after he stocks up on food. I.e. he's gonna get food, _then_ go see Twilight.]. Whatever people might say about him, in that moment, Anon knew he was some kind of genius.

For a newspaper building it was smaller than he'd expected. From the exterior it was probably one story, and wasn't too large. While the darkness made it hard to pick out much of the finer detail, the wooden walls and darker still wood floor gave it a rustic and cozy kind of feel. Past where he assumed the receptionist would sit, Anon found himself going down a hallway with 5 closed doors on the right side. [Numbers in text are weird (unless it's a big number) - use words, e.g. "five" - and also if it's not important, probably best not to mention it: "a few doors to the right", "a (long) row of doors on the right side", etc. Unless anon is some kinda Sherlok Holmes, he's not gonna instinctively count exactly how many doors there are (he might notice if it's just two, maybe three, in which case it's fine to say so, but five is too many) - and if he doesn't know, he's either gotta count (why would he do that), or you, the author, have to diverge from the narrator's POV to give this information - which feels weird, and on top of that readers will wonder what's the significance of this detail - see Chekhov's Gun.] The kitchen shouldn't be too hard to find. Assuming it was a kitchen where they kept the food. Do they call it a kitchen if it's in an office?

"H-hello?" a female voice called from behind the door farthest down the hall, coincidentally the one he was in front of. "Oh shitohshitohshit." [This sounds like the pony is saying "ohshitohshit". New speaker (or thinker) on a new line, and give some context to who's speaking/thinking]
She'd hear him if he ran and report it to the pony police. Was she getting up now? What if she saw him? Without thinking or agreeing on a strategy, his body betrayed him, and he began to speak.
"Hi, yeah."

It was over, he couldn't run now. Fortunately, she probably thought he was a pony. That was an advantage. Distinctly he heard movement in the room, which forced him to speak again.
"Ok, ok, wait. I'm, uh, I'm not some criminal guy. J-just don't come out, ok?"

"Real smooth, jackass" Anon thought

Understandably, the pony was confused.
"Is everything ok?" [minor detail - this can go on the last line just fine]
"Damn, she'd good [she's?]." he muttered.
Yeah, yeah, fine. Yeah. Don't come out. I just need you to trust me on something, ok?" [This could also go on the last line - just with some indication that he's not muttering anymore, e.g. "...he muttered, then called out: 'Yeah, yeah...' "]
"What might that be? Are you sure everything's fine?"
Sweat trickled down Anon's brow as he leaned against the door, prepared to hold it shut if the mare tried to exit and catch glimpse of him.

"Yeah, no. Things aren't fine. Just, uh. I'm not from around here. Like, I'm not a pony. I've got no money, nothing. Sorry, yeah. Just don't come out. Ok? You catch a look at me, you'll probably like go insane or something."
He['d] told her just about everything. Why he had gone and done that was a mystery to him. If she was speaking back, he did not hear[.]
For a second he let go of the handle to wipe the sweat from his face. His heart nearly stopped when he saw the knob turn.
[Other than the line breaks the dialogue is pretty good, doesn't feel much stilted.]