If you have all of your bits and pieces and plenty of time, putting a bike back together again should be the easy bit. If you've followed the single speed project ( Part 1, Part 2 ) you'll have a stripped down frame, a pair of wheels and a pile of bits leftover from when the bike was originally taken apart. At this stage its up to you to decide whether you're going to reuse some of these bits or whether your going to find some nicer, shinier bits for your new steed. I ended up using the same handlebars, but replaced the brake levers for some nice old school Leechi levers.
After stripping down the red frame I decided that the frame wasn't quite big enough for me, so I swapped it for this one which I had been using and had partially stripped down for repair.
The only difficulty using this frame presented was that the brake calipers I had didn't quite fit alongside the bosses for the V brakes that i'd removed- I therefore had to make a little adjustment by trimming the bosses down
For the next part you'll need for following tools which you'll have probably already used in the other parts. You'll need a chain splitter, a adjustable spanner, a socket ratchet and a 14mm socket.
You'll also need to source a single speed 3 piece crank and a 1/8" sized chain, which typically you'll find on an old 3 speed bike (you can pick both of these up used on ebay for a few pounds). Remember that if you intend to use the same axle that you'll need to get a cotterless crank.
Bmx's use a 1/8" chain, but although of a similar size for the purpose of making a bodged single speed the older chain seems to work better.
Now you'll need to loosely assemble your bike, I tend to put the wheels into the frame so that the bike is at standing height for me to work on- if you have a bike work stand you can stick the wheels on later. I also put on things like handlebars so that i can get the brake levers roughly in place and can begin to get a sense of what the bike is going to look like.
With this done you can stick the crank back on, make sure the nut is done up nice and tight.
Next, thread the chain onto the rear sprocket and over the new chainwheel and fix it back together again with your chaintool.
Finally, with your chain connected and your wheels loosely attached adjust the tension in the chain bike moving the wheel, when you are satisfied with the tension tighten the wheel nuts. Too tight and the chain will wear and snap, too loose and it'll just fall off.
All thats left to do now, is to fit the cables, properly attach and adjust the handlebars, brake levers, seat and post- you should now have a very basic but beautiful homemade single speed