The Sneak skill is a skill that involves detection, so you might want do these procedures while sneaking and undetected. Don't forget to activate the Thief Stone at the 3 Standing Stones and get a rested bonus too by sleeping in a bed. Also wear tiems that make the skill increase faster.
Sneak attacks are the best way of leveling the sneak skill since it also has to do with damage while being undetected which are very useful for assasins. Simpily sneak behind a person while being undetected and sneak attack them. They might start to find you so use a bow too [Also use daggers since they're quiet]. The Greybeards are the best way of doing this procedure since they don't find you when sneak attack them with a dagger, which is quiet. You can also do this to Hadvar or ralof in the beginning of the game too. There are a lot of XP earned when doing this and by far the method is the fastest.
Hiding from people
Another way is to find an area with people, and sneak against a spot where they can't see you [better if you automove]. Though this levels the skill slower than sneak attacking, you don't need to do anything but sneak against something. you can also do this with areas with creature too, and level up.
Training is another good way to level this skill, though it costs money. Simpily find a NPC who trains Sneak, train 5 times [unless before the 5th time, you lose money], and pickpocket the gold back. If you get a level up while doing this, you can repeatedly do this until the training gets to it's limit. The trainers are:
◾Khayla- Common, Khajiit Caravans
◾Garvey- Expert, Markarth
◾Delvin Mallory- Master, Ragged Flagon, Riften
Though you can't read the same books again to level the skill, these books help you level up the skill [not all they way to 100, but you can follow the other procedures above too]. The books are:
2920, Last Seed, v.8
Legend of Krately House
The Red Kitchen Reader