You will need the following things:
-wire for tying: pre tinned copper wire, I used 32 guage, you could probably go a little thicker, but I wouldnt do much. Radio Shack is where I usually find this. Theoretically any thin wire that will hold the solder will work, but this is how it has always been done, so this is what I use.
-Solder: Its better to use a low temp solder as it will expose the spokes to less heat stress, which in theory would be bad for them. I have used high temp silver bearing solder, and it looks great, but is a pain as it requires a higher heat not always attainable with low grade soldering guns.
-Flux: thick paste flux is best as it stands up to heat better and will let the solder flow really well.
-Soldering Gun: just about any will do, but I like to use at least a 40W gun to keep the job a bit quicker and easier.
-A Bike Wheel: can't tie and solder a wheel, without a wheel, now can we.
-This Instructable: well...duh.
Step 1: Build or Buy a Wheel and Ride It.
Step 2: Wrap the Main Spoke With Wire...aka Tie It.
First you start by lying the wire along the side of the spoke at the bottom of the spoke cross junction, I'd say 1/4 inch of wire would suffice.
Wrap the wire around the two spokes, pulling it tight and keeping the coil neat as you work your way down. You can work up too, just know that the goal is to wrap the wire around enough times to cover the junction and cover the initial little bit of wire you ran along the spoke. I wrap 7 times, 7 is a good number.
on the last wrap, before pulling the wire tight tuck the end between the two spokes, and inbetween the last two coils of wire. You will end up with the last coil of wire only wrapping around one spoke and then sort of "tying off" between the other wires. Pull the wire taught, and snip it as close as possible.
Repeat this at every spoke junction around the wheel. I prefer to tie them all first then solder them all, but I suppose you could tie and solder each one.
Step 3: Now, for the Soldering Bit
First, cover the wire on all sides with a bit of paste flux. You can do this job without flux, but its ugly, and not fun, so I do not condone it and will not cover it here. Flux makes your solder flow, and will make this job look good and a lot easier. If you don't wanna use flux have at it but you will be sorry.
Now that the flux is on, heat the wire with the tip of the iron by placing the soldering iron on the wire.
Touch the solder to the wire, but not on the gun. As the wire heats up to the right temp, the flux will bubble and soon after you will see the solder melt and flow onto the wire. Once it has flowed into the wire coil on all sides, you are good.
Too much solder and it will try to pool and drip, you want to just cover up the wire, if you can still make out the faint outline of the wire coil that is fine, if you can still see spaces in the coil you need more solder.
Don't bother touching the solder to the iron to get it to flow, this won't work, and typically just makes things messy.
Once you have soldered all your tied junctions you are done. Wipe off any remaining flux and get out there and ride.