False Grips:There is no way around it. To achieve the Ring Muscle-up, you MUST have a false grip. The false grip allows you to make the muscle-up transition from the pull portion to the push portion.
Chalk:To achieve and maintain a false grip, it is very helpful to have chalk. This keeps your false grip from slipping. Make sure to also place some chalk on the part of the wrist that will be in contact with the rings during the false grip.
Elbows tucked in: A common mistake seen in basically everyone that is learning the ring muscle-up is that they flare their elbows during the transition. This makes the movement almost impossible. The key is to keep your elbows close to the body. To perform the transition, imagine having your elbows touching your body while you lean forward and roll over the rings.
Negatives: Like any movement, you are trying to learn, Negatives are always a great way to get your nervous system and your tendons primed for a movement.
False grip pullups and Deep ring dips: False grip pullups and deep ring dips are great accessory partials movements for the muscle-up. Make sure to go deeper than 90 degrees for the dips because for the ring muscle-up you will be performing the push from a much deeper position. Practicing deep dips will strengthen the range of motion needed for the muscle-up and also ensuring you will also have the mobility for the range of motion.