I second the rec for charting - but your partner has to be on board and you have to be strict about it.
Even if you choose another method, I think it is important to be aware of fertility signs in general and to know when you ovulate.
During the fertile period, you can either abstain or use a barrier method. I abstain, and personally I think knowing I am fertile would scare me enough not to even take the tiny risk of a barrier method failure - I am very specific about when I do and don't want a pregnancy.
The book Taking Charge of Your Fertility is very good.
I do not like the concept of hormonal contraceptives unless there is some other medical or lifestyle reason to use them that can't be solved in another way, so I applaud your decision. I also think that as a woman it is very empowering to know what your body is doing.
Get used to me. Black, confident, cocky; my name, not yours; my religion, not yours; my goals, my own; get used to me. -Muhammad Ali