First and foremost, the most important thing I've learned. Try a glass (or crystal) nail file, they are the most amazing thing ever! Thin, peeling, weak, and easily breakable nails that you can't grow out past your finger tips? This may be the solution, it was for me. For years I thought it was impossible for me to ever have healthy, strong nails - but now I do.
~Where do I get one?
If you live in the US or Canada, get the Swissco brand glass file from Sally Beauty Supply (And buy a Sally's card, it's 5 dollars for a year and they give you a 5 dollar in store certificate for getting it, so it's basically free. On top of that it gives you a discount on everything in the store, so instead of paying $7.99 for the file, it will be like 5 something). Live outside the US or Canada? You can buy them from the websites TransDesign(they seem to be sold out right now -.-) and Head2ToeBeauty, they are both based in the US but ship internationally. These places have good reputations and are a cheap source for nail polish, treatments, etc.
Secondly, find a treatment that works for you. The same product effects everyone differently, so something that is well loved and highly recommended by one person may make your nails break like crazy. It's just a matter of trying them all.
~Where do I find these treatments and which are reccomended?
One widely loved basecoat/treatment is made by the brand Nailtek, it's called Foundation II and can be bought at Head2Toe Beauty or TransDesign. Sally Hansen makes one called Nail Quencher, I personally really liked this one until it became hard to find. Barielle has amazing products but is kind of a high end brand, with products costing ~$16 a bottle. Don't fall for that, go to TJMaxx, Marshalls, or Ross and search the beauty sections, you can find Barielle products for about $4.99 a bottle. This is one of the best kept secrets to nail care, IMO. People adore their Natural Nail Camouflage and Growth Activator. But I have never read a single bad review or even comment on ANY of their products. I don't care about brands, but Barielle is an exception. If it has the name on it, I am going to buy it. It's that awesome.
Wear gloves when cleaning! Please! Water and cleaning products do immense damage to your nails, so make it a habit.
Cuticles. It is recommended that you do not cut your cuticles, they play an important role in healthy nails. But you do want to use a product to soften/remove them. When I say remove, that doesn't actually mean REMOVE, it really means minimize. A good remover will soften them enough for you to gently push them back with a soft towel or cuticle pusher. There might also be dead skin and left over cuticle on your nail bed, the cuticle remover will allow you to gently scrap that stuff off, giving you a nice even palate for you to nail apply your treatment.
~What products are recommended and where can I get them?
Sally Hansen makes Instant Cuticle Remover, a widely loved product by many ladies. You can find it at most drug stores, it is in a clear/blue bottle. Sally Beauty Supply also has Blue Cross cuticle remover, a lot of people seem to like that too, but I haven't tried it yet myself.
Another important step in nail care is to keep your cuticles moisturized. This helps keep them soft, healthy, and manageable. Makes them look 10X better, too! Even if you wear nail polish all the time like I do, cuticle treatments are still just as effective. Healthy cuticles mean healthy nails.
~ Product rec's?
Sally Beauty Supply has Haken cuticle oil in all kinds of different wonderful scents. Others like a cream, so they use Burt's Bee's cuticle cream. I really like Barielle Intensive Nail Renewal Oil right now. Found it at TJMaxx for 5 bucks!
Lastly, do you like nail polish but hate the dry time? Get ready for this, it is life changing! Haha, I kid..but seriously this next product turned me into a nail polish FANATIC. Get yourself a fast dry topcoat. You apply it over WET polish. So do your basecoat, first coat of color, second coat of then, then right away apply the fast dry top coat. Not only will your polish be dry in under 10 minutes, it gives a wonderfully glossy finish.
~ Product rec's?
The one and only product I myself highly highly highly recommend is Seche Vite fast dry top coat. Get it at Sally's with your Sally's card, so you pay under $5 for it, instead of the tag price of $8-9. You can also buy Seche Vite at the above site's I've linked.
Where did I learn all this, and who are these "ladies" I talk about? The Nail board on Makeupalley.com(you have to have an account and sign in for this link to work)! There is even an account they made loaded with information regarding nail care, you can see it here.
So to sum it up...
Get a glass file
Find a treatment that works for you
Get something to remove/soften cuticles
Get a cuticle oil or cream
...And if you like to wear polish, get yourself a fast dry op coat!
That's it for now, if you have any questions I'll do my best to answer them. Hope this help anyone, and sorry for the wall of text!
EDIT: I thought I would make this post a little more fun by posting some nail art. I have no before pictures, but this is what they look like with all the proper care I outlined above.