The only big secret to grafting queens is eyesight
The first time I tried grafting was with a store-bought tool using store-bought plastic cups fresh out of the bag. I only grafted 6 or so cups and ended up with maybe 3 cells. Not a great percentage but not a really bad one either.
The next time I tried I first sprayed the cups with sugar water and placed the bars in a hive for 24hrs before grafting. I got a little better take on that one but I wanted to see if I could do better so kept experimenting with the variables. I went to home dipped wax cups, grafting larvae of various ages, grafting at different times of the year and during different flow periods and even messed with lunar cycles for a bit.
The things that probably made the biggest difference for me were:
1) Using natural wax cups (I still run trials between wax and plastic and wax beats plastic every time. Maybe not by much, but wax always wins.)
2) Homemade grafting tools. The ones that you buy for $10 or so are great for mutilating larvae. I can show you how to make a better one from a paper clip.
3) Using the right larvae. In theory any larva the is still being fed royal jelly should work (1-4 days from the egg) but in practice I find a better take from younger larvae (can barely see them in a pool of royal jelly) and you can estimate the new queen's emergence a little better if they are all about the same age.
4) The more young bees you have to build the cells the better. Something I learned not long ago, well maybe 2 years ?, from Alan Bukley was that you can start cells in a small queenless AND broodless nuc. Makes a lot of sense when you think about it if no brood the nurse bees have nothing to do but raise your grafts. Young bees is key.
5) Feed them whether during a flow or not. The more you convince them that they should multiply (swarm) the better.
We'll be going over this stuff at Bud's again this year with hands-on demos.