Spend your AA's. Open the tome. Read what it says, then close it. You'll notice a message that says "This is now your active codex." If you re-open it, it'll say something like "You are already learning from this codex." Close the window with the description in it.
Turn all your xp back to what was normal level gain to fill your tome. If you have it partially between that and AA's, it'll split. If you turn it all to AA's, it'll just do your AA's and not your tome.
If you move the bag your tome is in, it will close the tome. You'll have to re-open it to have the xp go into it again. If you share your toon, tell them to make sure your tome is active when they log on it the first time, and if they move your bags around.
A good mod to get is the TSS player window. It shows you tome/aa progress on your HP bar, so you don't have to open your inventory to keep seeing where you're at. I like it because I prefer the default EQ interface. Most of the others give me a headache or look like crap.
The first 1% of a tome is the absolute worst. Especially when you're on your first tome. You're going to be wondering the entire time whether or not it's working right, and it's going to seem to take the equivalent of a 10aa grinding session to get it to move enough so you can be sure it's working. If you get paranoid, just open your codex again and see if it says you were already learning from it.
You will not gain any bonus until you complete 10% of each tome. At 30%, you get 1% bonus. At 50%, you get 2% bonus. At 70% you get 3% bonus. At 90% you get 4% bonus. At 100%, you get the full 5% bonus. These are just marker points, however. Every percent adds a set amount, and you can view this amount on fomelo.
When you finish a tome, it will stay at 100% until you remove the tome. It's a good idea to buy your next tome and carry it around with you when you get above 90% on the previous one. That way you're not flipping out and needing a port to Erimal in the middle of a great group or raid.
Good luck!