General giving:
* donner (pronounced "don-nay") is the most common and general word for "give".
Giving a gift:
* offrir (pronounced "oh-free") is used for giving a gift or offering something.
Giving permission:
* laisser (pronounced "lay-say") means "to let" or "to allow", which can be used to express giving permission.
Giving something to someone:
* remettre (pronounced "ruh-met") means "to hand over" or "to give back" and is used for giving something directly to someone.
Giving birth:
* accoucher (pronounced "ah-koo-shay") means "to give birth".
So, depending on the context, you could use "donner", "offrir", "laisser", "remettre", or "accoucher".