I've changed bearings without special tools no problem. Some designs you can just tap them out using the axle or a blunt screwdriver. The new ones will usually go in easily enough also with a light coating of decent grease.
Go to the link Montgomery referred to - I can vouch for the quality of instructions that Dave gave - I printed them out and have used the instructions a few times since then as well. When knocking out the bearings I supported the hub on a pvc screw-on waste pipe fitting cap (the bit the tightens the fitting on to a pipe length). And don't be frightened to really wallop the drift - it takes some getting out!
To replace the bearing, use a socket from a spocket set, or a tube of some sort to fit the outer race and then put in a vice, this way you can control the movement and avoid bashing bits and breaking them.
I have one of those headsets. No you won't need to take the cup off...You will need to remove the stem and then slide the fork steerer out of the headtube. The bearing cartridges should then be easily removable with fingers - they might need to be gently prised out if the grease has held them in position. Clean them or replace them and liberally grease them/the cups and reverse the removal process to install. hope that helps.