You'll need a 13mm and 17mm cone spanners for the front and 15mm and 17mm for the rear.
For the front, pick a side and undo the lock nut with the 17mm cone spanner while stopping the axle rotating with the 13mm spanner on the cone near to the bearing seals. These might be pretty tight and they'll have a standard thread.
Take the nuts, spacers and cones off the axle and slide it out of the hub.
All the bearings will fall out and roll under your fridge at this point.
Don't worry as you'll be replacing these anyway. 9 bearings each side, and they are quarter inch in size.
Degrease everything, clean and check the bearing surfaces for any pitting of grooves. They should be nice and smooth and shiney.
Reassemble by sticking the bearings back in with some quality grease, and re-inserting the axle. Put the cone, washers and lock nut back on.
Then you'll need your cone spanners to tighten the lock-nut down without over tightening the cone onto the bearings.
This is the tricky bit.
It should run nice an smooth without any play in the bearings (too loose) or any stiffness (too tight). Getting the balance right can be tricky, and it often helps to put the wheel back into the bike and tighten the skewers up to get the bearings perfect.
For the rear wheel do the same, but start on the non drive side using a combination of 15mm and 17mm cone spanners.
If you want to remove the cassette body you'll need a 10mm allen key, once you have removed the axle.
Apologies for any innaccuracies as I've been watching the new girl on Countdown while typing this.
Just had a rethink: The front bearings might be 3/16ths of an inch. Can't remember without stripping my hubs down.