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Consider nail hardeners and growth gel. Take a Biotin supplement. Consider upping your protein intake. Don't saw your nails back and forth. Always use base and topcoat.
Let's set the record straight right from the beginning: Growing your nails actually means not breaking them. Generally speaking, you can't magically make your nails grow faster, but you can get the strong and less prone to breaking, so they stay long and beautiful. That being said, there are a couple of products that claim to promote nail growth:   Nail hardeners. These are clear "polishes" that use formalin (methylene glycol dissolved in water) as the strengthening agent. They're like nail polish, only with a shield and a machete.  Growth gel. Does it work? Well, maybe. Sally Hansen's VitaSurge Growth Gel says, "The multi-active bead infused formula instantly releases a surge of nourishing Vitamins A, C & E to nourish and treat nails for healthy growth." Multi-active bead infused formula? Sure. Take that for what it's worth. While it won't speed up the growing process, Biotin has been linked to stronger, less-breakable nails. If you suffer from brittle nails that just won't grow out, it's possible this could help. You might see a change in your hair and skin, too! This is available in some dietary supplements -- but it'll probably involve reading the "ingredient" label. Look for vitamins and supplements that claim to improve the look of your hair, skin, and nails; they probably have Biotin in them. It's a long-held opinion that your diet determines what your nails look like (amongst other things). Well, that's true to a point. The fact of the matter is that if you live in a first world country in today's day and age, you probably get enough of everything. So while a better diet -- more protein specifically -- can make a difference, take it with a grain of salt. "Not getting enough protein" is hardly an issue for most of us anymore, vegetarians included. That being said, it's never a bad idea to ensure that your diet is balanced for general health purposes. The more nutrients and vitamins you get, the better your body will look overall, nails included. If you're into long, beautiful nails, you've probably heard that there are right and wrong ways to file your nails. When you take your file or emery board to each finger, go toward the center on each side. It doesn't matter what shape you do, just make sure you go from right to center and left to center, not back and forth.  And while we're at the "don'ts," don't cut your cuticles, either. Push them back, sure, but don't cut them. That's your skin's last and final barrier against bacteria (it's on your entire body, after all) -- don't mess with it. Though it's ultimately a matter of personal preference, you may want to stick to round nails. Square one have more of a tendency to catch, ultimately breaking more easily and more often. If you're painting them, that is. It's probably best if they're bare (polishes can eat away at your nail), but we all know how tempting color can be. If you can't imagine possible having nude nails, always use base and topcoat. Just plain polish keeps your nails from being able to breathe, ultimately weakening them. Applying a base beforehand and a topcoat after provides that barrier and the topcoat keeps the polish looking good, keeps you from picking at it, and tops your nail off with a seal-like finish. Watch out for polishes that have chemicals -- they won't do your hands any favors. If it's something you're concerned about, you can find colors that are "natural," "vegan," or "chemical-free." Putting formaldehyde on your nails? No thanks!