I am trying to avoid pregnancy by not making love at "risky" times of the month. But one of my friends has told me it is actually possible to conceive during a period! Is that really true?

Yes, though it would be unusual. It's more likely to happen towards the end of the menstruation.

Really, your kind of "rhythm method" contraception should only be attempted under the guidance of a professional who is expert in natural family planning. If you can't find one, I suggest you use a sensible method, such as the coil, the condom, the Pill or the patch.