Grab the ring at the end of the chain in your left hand (I’m right handed, so I do this; I’m not sure if someone who is left handed switches and uses their right hand to hold the ring). Hold the ring in the center of your chest. This hand won’t move for the censing.
Next, grab the chain above the bowl of the thurible. If it only has one chain, leave two inches or so of chain before the bowl.
If the thurible has three (or more) chains, it’ll be easier to grab the chains if they’re all hanging down straight. Hold an inch or so above the “lock” that keeps the cover down.
When censing, while your left hand is holding the ring at the center of your chest, bring your right hand to eye level. Flick your wrist forward for a single swing. To separate “sets” of swings, lower the thurible to waist level, while keeping your left hand at your chest, and immediately raise it again to eye level.
Don’t forget different objects get different amounts of swings.