Slurs (more commonly called hammer-ons and pull-offs) should be performed with 50/50 effort between the fingers on the fret board. It takes the burden off of the pulling finger and keeps your hand in position. If you just pull with the one finger, your hand will want to turn up toward the head stock. If you're holding the string down with your index finger and pulling off with your ring finger, you will want to push with your index finger as well as pull with the ring finger. Of course, if you push too hard with the index finger(or push out of sync with the pulling finger) then the note held will go out of tune. The actions have to occur simultaneously. Pulling off to an open string rather than a fretted note is trickier.
At first you will have to really bend the string and then let it go, but over time you'll gain greater control, and it will just pop right off of the edge of your fingertip.