I've started a game recently with one of my characters as a human bard, stats 16 strength, 18 dex, 16 con, 18 int, 8 wisdom, 18 charisma. She is level 4 now, but it does not seem as though she can cast spells. I have had her write sleep, chromatic orb, and web into her spellbook, and she has them memorized, but when I go to the spell-casting bar (on the bottom of the screen) the spells are always greyed out, even when I would expect to be able to cast them.

Help?

As the other poster stated, if by chance your bard is wearing armor he/she will not be able to cast spells.

Excellent. Of course. Thank you.

I have the same problem, and my bard is not wearing armor. Any ideas?

If your Bard is not wearing armour, and the spells are greyed out, then you need to rest. Spells need to be refreshed by resting.