You can only get pregnant around ovulation. This happens about 14 days before your next period. The 14 days are however not accurate enough to base birth control on it. It is also only true for cycles in the 24 to 33 day range and it can move by a few days every cycle. Sperm also stay alive inside you for 3 to 5 days. When you finally ovulate this sperm can take their opportunity to fertilize the egg. So in all there is probably a 8 day window where you don't want to have unprotected sex at all. It is however difficult to determine this window accurately because you can not go back 3 days and undo sex you had when you ovulate and the ovulation date can move around.

You are fairly safe if you have unprotected sex during your period if you do it in the first few days, not the end and you have cycles of around 28 days.

It is easier to get infections during your period but if everything is clean and healthy, that should not be a problem. If neither you or the man mind the mess, go for it.

Wash up, have sex on an old towel and wash afterward. Better still, make it a fun shower time. Never have sex with a tampon still in you. Menstrual flow is also not a very good lubricant so you might need some extra lubrication.

You can get menstrual caps that you put up against the cervix that will catch the menstrual flow during sex and it will save the environment from some pretty evil and bleached menstrual products.

If you can absolutely not afford to have a baby, use condoms.