Boilinfrog - hi, when I've had my blades sharpened at the local shops, they use a bench grinder with a fine grit stone wheel. They hold the blade so that the sharp edge faces the same direction as the rotation of the wheel. That is, if the wheel is rotating counterclockwise when you look at it from the side of the grinder it's mounted on, the wheel is spinning down towards the floor - so the sharp edge of the blade faces down towards the floor.
If you have one of those mulcher blades where the main blade is split in from each end to create the mulcher portion, then you may have to use a Dremel tool with a fine grit stone bit to get into that small area. You still want the wheel spinning in the same direction as the sharp edge of the blade. If you have a blade that's bent/curved so the mulching part is still along the same outer edge - it can all be done via the grinder.
Either way - if you're sharpening your own blades, remember to check the balance of the blade afterwards. If you take too much metal off one side or the other, you'll make the blade unbalanced and when it's back on the mower, you'll soon be able to tell something's wrong. (Especially if it's a push mower - your arms will get real sore as you fight it!) One shop that did my blades in the past would re-balance the blades by taking a little metal off along the back edge of the blade, opposite the "light side" of the blade, using the grinder.
For me, it's been much easier to simply find a hardware store or lawn/garden supply store that can do this and take my blades to them. (They'll charge different prices so you may want to call around a bit first and get estimates based on the size/type of blades.) Because they can't always do the blades while you wait, I always invest in a spare set of blades and keep the spare set sharpened. It's easy to swap them out and be able to continue mowing while the other set get sharpened. I hope this helps - regards! Jim D/West Point, VA