I only braid my hair at night after it has a chance to dry.I've found that if you braid your hair when it's dry, it helps relax your curls a bit while you sleep. If you do it when your hair is wet, our hair is so thick it usually can't dry in the braid. So when you unbraid it in the morning, it may still be wet, so it finishes drying and can draw up—not that that's a problem, unless you are wanting to show more length with your hair.

What I'd suggest is to braid your hair up at night when it's dry. If you want, you can put a little olive oil or some other light oil like coconut oil or jojoba on the ends. Don't comb or fingercomb, just smooth it on and braid it in a low braid or two.

In the morning, after you unbraid your hair, then you will have a chance to refresh all your curls. To refresh your curls, wet your hands, run them over your hairline and the ends of your curls. Add a little combing conditioner to your hands, rub them together, then smooth them over your hairline, ends, and any fuzzy parts. It's best to not soak your hair. It should just be slightly damp when you are done. This helps smooth your curls, but lets them stay stretched out a bit (if you don't soak your hair, tha is), and it gives your hair more conditioning.

Now, if you are wanting a more set look, I'd definitely let it dry before braiding it up. Once it's dry, you can then mist it lightly with water before putting it in braids or twists to set it. Again, our hair is so wonderfully thick that if it's actually damp, it often won't dry by the time you get up in the morning. And especially if you are trying to set it, you don't want your hair to still be damp when you undo it in the morning. Your hair won't really have gotten a chance to set because it only really sets when it's totally dried in the set position.