Here are some tips on the gymnastic rings

Ring Pushups: (Adjust straps so they are about 6" off the ground) Work up to as many as possible, if you can't do at least three good reps, raise the straps. Hold the bottom position for 3 seconds on each.
Ring Dips: These are difficult at first, so if you can't do a full dip, hold yourself in various positions for as long as you can. This exercise is important to the muscle-up and builds the chest muscles. Have the straps about waist level and lower until the elbows are bent to 90 degrees.
Ring Rows: This is the key to the muscle-up, but if you are not strong enough yet do these to build up some upper back and arm strength then you should practice. (Adjust straps low enough to lay horizontally under them, with room to lower your body and raise it all the way up, not touching the floor.) You should be able to knock out several repetitions.
Isometric Hangs/ Hanging Leg/Knee Raises: These are great for building up the muscles needed to initiate powerful pull-ups. For isometric hangs, engage the shoulder blades as though you are starting a pull-up, then hold it there for 10-15 seconds and do several sets of this.