I worked in bike shops through high school and college. In that time I learned to build bicycle wheels. Some people find the idea of building a wheel intimidating but it isn't that hard. I'm going to show you how to build a wheel that has a radial pattern on one side and a more standard crossing pattern on the other side.
The most important thing is to be certain that your spokes are the correct length for your hub and rim.
I did this at TechShop in Menlo park with regular tools, no special bicycle tools were necessary.
Step 1: Lay out the parts
I laid out my parts and tools on the table so I could decide how I was going to approach this build. Since the one side is radial laced and the flange is smaller it is the best side to start with.
Step 2: Insert the spokes - side one
Since the spokes won't cross on this side we will insert them all in the same direction. You might think we would go from inside to outside but you'd be wrong. It would be the easier way but that's not how we will do it. We want to see the spoke heads on the outside so we will insert the spokes from outside in.
This presents a problem as the spokes will hit the other larger flange. To get around this you can push the spokes with your fingers as you push down or just pull them where you want with a pair of pliers. Do be careful to bend the spokes as little as possible during this step.
In the pictures you can see the different ways of inserting the spoke and how I went about the task.