Start by using the upper hole in the dogbone, the lower one will have your fully extended body in the plane of the tramp when you're erect, with back straight. Which is a position that maximizes your overall resistance to heeling. But you'll do fine initially with the upper hole, and it'll feel more secure to you at first.
To prepare to go out on the trapeze, I let my but hang over the gunnel and put my weight onto the dogbone. I rotate my upper body so that I can get my aft foot onto the gunnel, and then with all my weight on the trap wire, quickly push my torso out away from the boat with that rear leg, and then plant the forward on the gunnel as well. All done without hands, which are occupied with the tiller and sheet. And then move fore or aft to trim the boat.
In the process of extending your leg, you'll be letting the tiller extention and the mainsheet slip (in a controlled fashion)thru your hands to maintain course and mainsail trim.
It'll all seem awkward for a while, keep practicing and it'll become second nature. Coming back in is the reverse. Forward leg remains straight, and slides across the hull and tramp, so it can slip a foot under the hiking strap if necessary, and the rear leg bends and the upper body rotates til your but hits the gunnel. Then the aft leg extends onto the tramp, and you adjust your seating position on the windward hull. Then you can unhook if tacking/jibing.
I'm sure this varies amongst catsailor, but the key is put all your weight on the trap early, and trust it. Trying to bear some of you weight on the handle just increase the chances that the dogbone will unhook. Happy sailing!

Dave