How can I steal items without being put in jail and keep the item?

Can I steal items without being put in jail and keep the item? What is the name of the skill for it?

To steal something without being prosecuted, you have to be in sneak mode and undetected (the "eye" symbol must be closed).

So the skill you are looking for is Sneak. However, even with a low sneak skill stealing is very easy when no one is around who could detect you. You still have to enter sneak mode though.

The item you took will still count as stolen, so if you go to jail later for another crime, it will still be taken from you. It may also happen that the owner of the item sends some thugs after you who will try to kill you, even if no one saw you committing the crime.

If you join one of the factions (Stormcloaks or Imperials) the guards of that faction in the cities will allow you to pay them off, typically some fraction of your current bounty, and they will let you go no questions asked.

Keep in mind too if you steal something that is very useful to you (a sword / dagger / armor, etc), if you are caught by a guard for any other crime, they will confiscate that item off you.

Just remember that, in case you get caught and find out later you lost your favorite item, etc;