If you are lucky enough to beg, borrow, or steal the special tool used by the Dealer, it is a simple process. But if you don't have the tool, like me, it's a bit more involved. Here's the "poor man's" process that I use:
1. With the engine cold, remove the spark plugs and valve cover.
2. With a big wrench or socket rotate the engine until some of the the cam lobes are opposite the lifters and measure the gap with feeler guage . Write down the gap (or lash) for each of the lifters, i.e. I1 thru I8 and E1 thru E8. Repeat turning the engine until you have measured at each lifter. It's a good idea to recheck all of your measurements, believe me.
3. Determine which, if any, are out of spec. Figure out what thickness of adjusting disc is needed to bring the gap (lash) into spec. Match what is needed to the various thicknesses offered by Mazda (I have a list of part numbers) and order the new discs.
4. Once you have all the required new discs in hand, remove the timing belt and the cams. Remove the old, out of spec discs and replace with the new discs.
5. Replace the cams and the timing belt. Put some oil on all the cam lobes and rotate the engine by hand several revolutions. Recheck the lash like you did in #2 above and pray that everything is in spec like it should be.
6. Replace the valve cover, guzzle a couple of brews, and pat yourself on the back for a job well done.
The main advantage of having the special tool is that you don't have to remove the timing belt and cams. The tool somehow enables you to depress the lifters one at a time and remove/replace the adjusting disc with the cam in place. I understand that the tool costs something like $400, well worth the price for a Miata mechanic, but out of reach for most of us shade-tree mechanics.