recent college grad in a NYC apartment (small kitchen, no appliances) - needs to cook easy (inexperienced), fast, and healthy food

Here is one of my favorite food52 recipes. No special equipment or skills needed. You can easily serve it at any meal, eat hot or cold, fits in with the healthy idea, travels well for lunch.
https://food52.com/recipes/14244-quinoa-and-kale-crustless-quiche

A little fiddly until you get the hang but this is delicious, can be a starter or main, you can use all prepared ingredients (washed lettuce / canned mango / cooked shrimp) or make fresh and all you need is nimble fingers for wrapping! https://youtu.be/xYt9gYii1kw

Clarification - small oven, microwave, and blender but no food processor, crock pot, immersion blender, etc. The bare basics.

Learning to make good stock/broth from bones is a great place to begin for a new cook. It becones the beginning of many meals.

By "no appliances," what do you mean? No oven/fridge? If that's the case then your first investment should be in a single burner hot plate.

But either way, start experimenting with basic but versatile ingredients (pasta, rice or other grains, beans, potatoes, canned tomatoes, onions, fresh garlic, fresh herbs, chicken stock, and your pick of proteins). These are all ingredients that can be combined in tons of different ways to make different dishes. If cooking meat feels daunting a great option to start with are packs of pre-cooked chicken sausages (you can slice them, sear them, and put them in any dish). Pretty much every grocery store carries them.

Start to teach yourself basic techniques: pan-searing, roasting, boiling/steaming. If you learn how to do these three techniques well you can apply them to almost any ingredient and make yourself a pretty tasty meal.

Learn how to season food with coarse kosher salt and fresh cracked pepper! Get rid of the table salt (nothing that says iodized on it). I can't think of a single thing I cook that doesn't have at least a tiny pinch of salt in it. Learn to season food as you go instead of adding all the salt and pepper at the end.

This is a great food52 article on basic cooking techniques: https://food52.com/blog/10941-the-essential-techniques-that-every-home-cook-should-know

And I think this is a pretty good and "healthy" collection of one-pot meals. I also have a tiny, tiny kitchen and cooking one-pot meals is my saving grace. These are basic recipes that use basic techniques and simple ingredients. Some of them can be a little bland so experiment as you go and as you start to feel comfortable, expand! http://www.realsimple.com/food-recipes/recipe-collections-favorites/quick-easy/one-pot-meals

You might also consider taking a class at a cooking store. Williams-Sonoma has classes that range from free to over $50 (paella for 2 with a free pan this month); call the local store for info. Sur La Table has classes almost every day, which run about $70-85 but are hands-on and sometimes include a pan or utensil, and they also have a three-part series on learning basics for $210...pricey, but maybe someone could give you that as a gift?

Start with a basic cookbook--some classics are Mark Bittman's 'How to Cook Everything' (he also has a 'Basics' book); 'Good and Cheap on $4 a Day' by Leanne Brown; 'The Joy of Cooking' ; ’Good Housekeeping's Illustrated Cookbook' (I have the copy my grandfather used to learn how to cook as a 78-year old widower); or even Betty Crocker's Cookbook. The last three have been around for decades, so you can probably pick up a used copy for cheap (try The Strand).
Some basic equipment is helpful--a 2quart pot, a 6 quart pot (I have one with a strainer in the lid, a cinch when cooking pasta), an 8-inch frypan or saute pan, a wooden cutting board, a paring knife and a chef's knife (Victorinox is a sturdy and reasonably priced brand), a two-cup Pyrex measuring cup, a set of nested measuring cups and a set of measuring spoons (avoid ceramic ones--go for metal), and a serving spoon. You can go to a kitchen supply downtown and pick these up for cheap.
Easy enough to brown some ground meat, add in a can of crushed tomatoes and a garlic clove, salt, pepper, and oregano, and serve over pasta...or toss the noodles with some sautéed broccoli, pine nuts, and Parmesan.
The great thing about cooking is that if you make a mistake, you can eat the evidence ;-). I'm sure you will do fine!

I think this article might have what you're looking for! https://food52.com/blog/12996-17-recipes-for-the-recent-college-grad

Check out the "Looneyspoons Collection Cookbook" Their recipes are easy and on the waistline and budget also. One of my favorites is "Wowie Maui Chicken". A sweet and sour chicken and pineapple dish with rice. Cooks in 1 pot and makes leftovers for lunch or additional dinners. The recipe is all over the internet. Try it out, if you like it check out the rest of the book.

I was on youtube and clicked on this site "mind over munch" because i have a friend with limited cooking abilities who has some pretty big health problems and needs to eat healthier. i hope it helps. also, if you can read a recipe and stay away from high caloric, lots of dairy/butter and processed foods you will be better off. here is the site: https://www.youtube.com/user/MindOverMunch/videos