Firstly, head to a nail bar and have a luxe manicure; this will give you a good starting point. During the mani, make sure your cuticles are tidied but not cut (cuticles seal the point where your nails join your fingers, they protect the nail and hand from infection).
I have pretty weak nails, but saw a great improvement when I started using Sally Hansen Hard as Nails, £4.75. Where my nails used to split and flake they're now much stronger. I noticed an improvement in just two weeks and I now use it as a base coat. Wear it everyday to protect your nail - a polish-free nail is vulnerable to the elements.
If your cuticles are in a bad way: think dry, flaky with more than a few hangnails then you need to start nourishing them. Your cuticles protect your nails, so if you want strong nails you need good cuticles. I massage them every day with Elizabeth Arden 8 Hour Cream Skin Protectant, £25. This increases blood flow to the nail area and will gradually repair your cuticles.
A good diet full of nail-friendly nutrients will work wonders too. Make sure you are eating plenty of protein (it's the building blocks of healthy nails); Vitamin B12 will help keep nails healthy (found in fish, chicken and dairy); essential fatty acids (flaxseed, oily fish, nuts and leafy vegetables).
Biotin supplements (£4.29 at Holland & Barrett) have also been known to improve the strength of weak nails, take these every day. Plus, if you suffer from hangnails you may be deficient in Vitamin C and Folic Acid, so take these in supplement form to see if the problem improves.
Oh, and always wear washing up gloves when you do the dishes (or get your boyfriend / flatmate / parents - delete as applicable - to do it instead).
