The cup and cone hubs are very easy to service, and if you regularly replace the bearings it will increase the life of the cups and cones, obvously it is also easy to replace the cones.
You were right with your first comment, only remove the lock nut, washer and cone from one side, and then slide the spindle out with one set of cone/lock nut combination still fitted, the link below will take you to Shimano's technical documents, obviously you can then find the correct exploded drawing of your hubs, if it's a rear hub, it is easier to remove the free hub as well.
http://techdocs.shimano.com/techdocs/index.jsp
If the bearings are still well greased then they will stay in the cups, if they are dry they will fall out everywhere, but don't worry, replace them. The good synthetic grease like this link
http://www.wiggle.co.uk/p/Cycle/7/Finish_Line_Synthetic_Grease_35oz_Tube/4000000036/
is ideal when you rebuild the hub with new bearings. The only special tools you need are cone spanners, and a cassette remover, one important tip, don't get grease or any thick oil in the free hub, it will clog the paws, and then it will freewheel both ways.
However for a good bit of information, try this link, even now he's left us, Mr Brown can still be a great help.
http://sheldonbrown.com/cone-adjustment.html
IHTH
Have a go, shout if you have problems/questions
Giles