What kind of press are you using? Does it have heat? A floating makeready is where you tape a piece of paper to the platen. I like to use 25% rag bond paper. The counter for the die is taped to the die or if it has locating pins use those. Close the press up on impression to release the counter. You can use a spot makeready sheet under the paper to build up low areas. I usually cover the counter with a piece of mylar. If the mylar is too thick it will take some of the depth out. You will also want a makeready sheet under the platen. 

I’m sure this is moot by now, but I’ve done lots of embossing, so I thought I’d chime in. I often use a floating makeready, but I like to use a small piece of tympan paper for the base, because it’s strong and stable. Tape down all four edges securely before you stick the counter-die to it, and then slit one edge so you can slide small pieces of press packing underneath as needed. It’s nice if you can have .002″. 003″ and .004″ packing on hand. A thin sheet of mylar on top is handy to help preserve the counter, but it isn’t necessary and can reduce the crispness of the emboss. If you’re having trouble because you’re on the back edge of the platen and can’t get enough pressure, then you’ll need to mount some bearer blocks at the lower edge of the form to balance the load on the platen. 

Yes. The counter actually tends to slip into place, not out of it, as long as it hasn’t been forcibly shifted. 

On jobs with combo dies, where I’m foiling and embossing at the same time, the integrity of the counter is critical, and I’ve used floating makeready then. I also buy two counters for those jobs, because they’re cheap when the die is being made, but hard to make later if you smash a counter.