A women can get pregnant any time during intercourse. It has been said that during a women's period she can not get pregnant and I do not know of anyone that has but I would not try it, unless you are trying to get pregnant.
Anytime after they hit puberty basically. In some rare cases a woman get get pregnant while on her period. Though some days you have a higher chance than others.
There are several websites that you can use to help predict the right time. Simply input your info and it calculates your best days for ovulation. Normally it is approximately 14 days after the last day of your menstral cycle, depending on your cycle length.
A woman can only get pregnant when she is ovulating. If that person wants to know what days of her menstral cycle she ovulates she can take a ovulation test. The tests are available right by pregnancy tests in many stores.
Someone can get pregnant at any time, actually, because there are "iffy" times all during the period, so no one days is safe (even in the middle of the period)!