How do they work? It seems whenever I use them my skills don't increase. Is it just a case of waiting for a certain amount of time for the skill to increase or am I missing something?

They add a certain amount to your skill usage counter. Normally this is enough to raise the skill (especially if the skill is less than 50 or so), sometimes it takes extra practice to get over the threshold.

Either way, you have to rest or fast travel before you see the skill increase--skills increase only under these conditions:
1. you have racked up enough practice (uses)
2. You have just finished travelling or resting
3. It has been at least 6 hours (in-game) since the last time the skill has increased.
All must be true!

Thank you very much for explaining that to me.