Several methods to lap, JH. The easiest and the one I mostly use is to lube some cull bullets with fine valve grinding compound and shuck them through. I use Clover 320 grit to start and four or five cull bullets and when the first one comes out the top, I run it through again. When each bullet has gone through five or six times and they are going through easily, stop, clean the die and the post, and run a nekkid bullet through. Measure that bullet to see how far you have gone. If you're close to where you want it, lube a few more culls with 600 grit to polish.
Some folks wrap a piece of auto body paper around a dowel and just roll the die across a mouse pad using the dowel as an axle and applying some downward pressure. I've never done it that way, but many have.
I have used the dowel and the sand paper with the sizer in a lathe. Never opened up a sizer more than .002 and suspect that .003 would be the absolute most I would ever try for.
You can also open up moulds with the same compounds if you have a means of getting a machine screw centered and straight into a cull bullet to use as a shank. You coat the bullet and turn it by the shank in a tap wrench or the like while gradually applying pressure to the mould handles. I have a very neat gadget I got from Brownell's that is just a drill chuck on a wooden handle that works very well for this. Don't try using power for this unless you have a lot of experience and a very solid set up.
If you just use 600 compound, that's the best method I know to get a baulky mould to drop bullets freely. When you do that, you are not trying to remove any metal but the tiny burrs that the fresh castings are hanging up on.