It is not 'normal' in general for sex to hurt. As a poster above mentioned the vagina is able to relax enough to allow a baby to pass through it, it should have no trouble with a penis.
However, anxiety or nerves about pain or anything else during your first time means a lot of women find it hard to relax their vaginal muscles. For lots of women this eases with time. Some women have vaginismus (I happen to be one of those) and need to overcome this in order to move past it.
Have you ever inserted anything else such as a vibrator or a tampon? If not I'd definitely recommend exploring those, alone at first and then with your partner. There should be no rush to have penetrative sex, and if you explore things first (and properly - it can take months) then everything should be fine. If you continue to have problems I recommend going to your GP who can refer you to a gynecologist. They can check there are no underlying physical causes and, if you do have vaginismus, refer you to further help.
Please feel free to ask if you (or anyone) has any other questions!