To get better you need to look at every part of a quest in a sneak only manner. Look out for opportunities to sneak as there are millions throughout the game.
When sneaking, archery is your best friend as it lets you attack from afar whithout being seen. Another tip is the firing an arrow at a wall near an enemy will draw his attention to the spot and opens your oppotunity for an attack. Note that at the begining of the game you should chose the warrior stone over the theives stone as sneak attacking will be a lot more important than sneaking around somebody.
It is also important that you use light armor over heavy as it lets you move quicker whilst sneaking. Remember to take your time whilst sneaking as going to fast whilst near an enemy will alert it.
The best idea for a newcomer to skyrim is to head straight to the thieves guild. This is located in riften aand once your trigger their quest line you will receive the theives armour(light) after running a few errands for the leaders. Note that a certain degree of combat skill is required to reach the theives guild as some enemies are around that area.
Whilst attacking forts, camps and other locastions you should remember, as a theif, NOT to charge through the front gate. Instead, approach the location from hilltops and inconspicuous areas. Water is your friend and hiding beneath it is very benefitial. The best tip is to get up on a hilltop and rain down arrows.
The most important thing you need to know abotut sneaking is that when an enemy is looking for you (half eye open) they will go towards the spot from which you got their attention! There fore you should get away from the place that you fired a shot until you are hidden and then repeat your process.
Forget about daggers and two-handed weapons; sneaking is all about archery!