Mister C,
Lapping rings is pretty easy. Mixing the compound is up to you. I just dip my finger in and always end up with plenty on my finger. First step is to make sure your base and rings are secured to the proper torque specs. I always use loctite as well. If you are using dovetail type rings make sure they are as straight as possible. You can do this by using the lapping bar prior to applying compound. Hopefully you are using weaver or picatinny style rings as they are much better.
Place the firearm in a secure setting like a vise or clamp style cleaning station. It needs to be totally secure. Rub a bit of compound on the lapping bar and set it in the rings. Be careful not to get any compound in the screw holes. Add the top half of the rings and finger tighten the screws as evenly as you can. A good way to do this is to use the bit only if possible. If it is too tight you will immediately know as the bar will not move.
Gently move the bar perpendicular to the weapon to start the bar. Once the bar moves freely, move the bar parallel to the rifle. When the bar has little pressure remaining, this step is done. Remove the ring tops and bar. Use a towel and clean off the inside of the rings, once again being careful not to get any compound in the screw holes. Now you can see what you are working with. The lapped part will be obvious. The rings might lap very evenly or not even at all. The price you paid for the base and rings makes little difference I have found.
After this first lapping, or (test), you can get down to business. Place the coated bar back in the rings. Continue to lap until you get little pressure. Take the bar and ring tops off and clean them with your favorite cleaner. Place your scope in the rings, install the top halves checking the clearance between the two halves. If you lap too much, no space will remain between the rings and they will be ruined. Continue the procedure as needed. Lapping is a slow process of give and take. You can lap as much as you want as long as you leave at least 1/16 of an inch between the rings.
Things to remember:1. Aluminum will lap much quicker than steel. 2. Lapping compound and screws/holes don't mix. 3. Once you think you have all the compound off the rings, clean them again. 4. Once you remove material you can not replace it. 5. TAKE YOUR TIME. 6. If you don't, you will end up throwing your first lapping project in the trash. 7. You can usually take a cheap set of rings and lap them into a great set. 8. If your bar binds, moving it perpendicular for the entire process is acceptable. Just make sure to move it around a bit or you will ruin your bar. Have fun