Well first of all...what was it your reentry code?
If it's a 4...I'm afraid you can NOT reenlist (in to any branch.)
If it's a 3...you might only be accepted by the Army National Guard.
If you completed basic training before, you will not need to attend it again. However, if you were discharged while in basic...afraid you'll have to start from day one.
I believe you can reenlist in six months from your discharge date.
-LIFE