To do a wheel; you will need some sort of trueing stand. Some people can just use the bike frame (upside) down, some need a proper trueing stand. I am somewhere in the middle, and built my own:
http://forums.bikeride.com/thread-3155.html
Given that you have had two spokes go, you should replace them all, as more will fail soon. It is easiest to replace them one at a time. I like Wheelsmith spokes, and there are other good ones out there. Make sure you get stainless steel spokes, they are slightly magnetic near the bends and other forming. The other common spoke material is called UCP, and is very magnetic all over. The stainless spokes are about 5X stronger than UCP. Nickel plated brass nipples are much easier to work with than alloy.
A good spoke wrench is more important than one would think - I like Park, after trying a few others.
Generally, the spokes on the rear wheel are different lengths on each side. On front wheels without disc brakes or something else that causes an offset, they are usually the same length on both sides.
Lubricate the holes in the hub or the buttend of the spokes, and the nipples (inside and out) before threading the spoke. I use a very light oil that has a lot of solvent in it which leaves are very thin lubricious layer. It was in the bike section at Wal-mart.
To get the freewheel off, you need a FR-1 tool. There are many options out there, I have a cheap one, works fine. I use a large bench vice to hold the tool (on a very heavy bench). It is easiest if the tire is still on the rim, and fully inflated. Make sure you turn the wheel the correct way. I end up looking at it for awhile, considering which way the chain will pull the freewheel while I am riding, then crank on it in the opposite direction. It will take 100+ ft-lbs to get the freewheel off; which if you go in the wrong direction can wreck things.
Once you get the freewheel off, you should clean out the hub. Replace the bearings with new balls; usually ¼" in rear wheels, but measure. Check the condition of the cones on the spindle, and in the hub visually. If the ones in the hub are shot - new hub in most cases, cones on the spindle are replaceable. I use boat trailer wheel bearing grease in the hubs, bottom bracket and headset - inexpensive, water resistant and lasts. Once you get the wheel so that it spins smoothly and for a long time, you are ready to work on the spokes.