What effect do magic potions have? They seem to do nothing when I drink them. I was thinking they would restore my spells after I've used them up, but they don't.

You need to identify them to find out what effect they have. Use the "detect magic" spell to do so.

Most potions you will find are healing potions of some sort.

Okay now I get it. Man this game has a steep learning curve. This aspect is really frustrating since identify spells cost so much.

Really? I didn't know detect magic could be used in such a manner. I thought it just identifies items on the map. How do you use it on scrolls and potions?

The 0-level spell 'Read Magic' is used to identify scrolls and potions.
Make sure the scroll/potion is in your mage's inventory and then cast the spell from the radial menu. You'll be taken to the inventory screen. Select the unknown scroll/potion and you'll see a spell animation. Then go back into the inventory to see what it is.

Yes Read Magic is the spell to use. Half or more of my level 0 spells are that. Or if I need to rest for a cycle or 2, I will memorize all Read Magic and spam it. Then you can start stacking all those cure potions!

After going a bit forward, read magic is almost the only 0-level spell to use, with a few cure minor wounds in store to stabilize dying companions.

And yeah, the learning curve is steep as heck, even with prior D&D experience.