When I discovered I needed a new faucet for my laundry room sink I didnt want to choose between a cheap faucet that will only last a few years and an expensive one. I decided to build my own.
The faucet is made from 1/2" copper pipe and solder fittings, two ball valves, and two 3/8 threaded fittings.
The specific pipe lengths, configuration, and installation will vary based on your needs and tastes so I leave that for each person to determine what will work best in their situation.

Step 1: Tools and Materials

Tools:
Drill and drill bits
Hand saw
Tape Measure
Combination square
Pipe cutter
Mallet
Wrench
File
Steel wool
Pliers
Safety glasses
Heat resistant gloves (not pictured)

For soldering:
Wire pipe brush
Sand paper
Torch
Solder flux
Solder
Brush (for applying flux)
Lighter

Materials
Wooden blocks (One 8 in length the other 3-1/2 in)
Bolts of greater length than the width of the block
All pipe materials have 1/2" solder joints:
2 Ball valves
3 90 degree elbows (I bought extra in case of problems with soldering)
1 T-joint
2 3/8 threaded converters for attaching supply hoses
1 3/8 pipe thread to 3/4 hose thread adapter
Copper pipe

Step 2: Building the Base

The spacing of the supply hookups on a normal faucet is 4". You want to ensure that the pipes go through the existing holes in your sink.
Begin by using the combination square to draw two lines at 2" from each side of the 8 board. Then mark the half way point of each line. Use these points to center the 1/2" holes. Once these holes have been drilled use a hand saw to cut from the end of the board into the hole.
Mark 4 spots on the edge of the board in equal locations 3/8" from the edge and in the center. At each of these locations drill a hole that is large enough for the shaft of the bolt. A larger hole will provide more leeway and will be helpful in ensuring that the two holes line up. A drill press will be very helpful in this step but a hand drill and a steady hand will also work.
Once the holes are drilled push the bolts all the way through, attach the nuts, but do not tighten them yet.
As the base will often be exposed to water sealing and painting will help prevent decay and increase the life span of your faucet.

Step 3: Pipe Cutting and Fitting

The Pipe cutter I used is much larger than necessary. A hack saw will also work fine. Measure all of the pieces carefully to ensure that project fits together well. Compare lengths of pipe that are intended to be the same size to ensure symmetry.
To solder the joints:
1. Observe safety precautions. Read labels on the solder and flux and follow the listed safety procedures. Always wear safety glasses and gloves. Work in a well ventilated area as flux and solder can produce toxic fumes. Use lead free solder to ensure no contamination of the water in the faucet or to you during assembly.
2. Wire brush the fitting and sand the pipe
3. Wipe both clean
4. Apply soldering flux to both surfaces to be soldered, be careful not to over apply. Avoid skin contact by using a small brush.
5. Fit the pieces together.
6. Heat the pipe and fitting with the torch
7. Move the torch away and apply solder. There should be enough to go all the way around the pipe. Be careful not to over apply.
8. Observe caution as the pipe will be very hot. And the solder may remain soft until it has cooled completely.

Step 4: Assembling the Pipes and Fittings

The exact length of the pipes used will depend on the specific situation. Start by connecting the 3/8 threaded fittings to two equal lengths of pipe. Press the unsoldered end up through the holes in the base so that the threaded fittings are on the bottom. Make sure the length of pipe above the board is equal and tighten the bolts.
Attach the valves making sure that they both have room to turn freely.
Once the valves are in place connect both to the T fitting using elbows. The center of the T fitting should face forward as this is where you will attach the pipe that caries water to the sink. Use a piece of pipe to ensure that it does not interfere with the valves.
Fit an elbow onto the final piece to direct the flow of water downward. Adding a 3/8” threaded piece and the hose adapter will allow you to screw hoses onto your sink.
It is wise to cut and fit all pieces before soldering to ensure they all fit together properly.

Step 5: Testing

The 3/8 pipe thread to 3/4 hose thread will allow you to fit a garden hose to the bottom of the faucet. This will allow you to check one side at a time. Connect the hose, you may need a coupler as both ends will be male, and check for leaks. Wiping the faucet dry will ensure you spot any problems.

Step 6: Cleaning Up the Copper

A file will let you remove large pieces of solder that may have dripped during fitting. Steel wool will clean the copper without leaving harsh or obvious scratch marks.

Step 7: Installation

After you are satisfied that the joints are sound and the faucet looks attractive you can install it in your sink. Shut off the water and open the old tap so the water can drain. Shut-off valves are notoriously problematic use penetrating or a lubricant (such as WD-40) and be careful not to turn it too hard. Forcing a frozen shut-off valve can lead to serious troubles.
Fit the pipes through the holes in your sink and make sure the base sits flat. You can use the third hole, often used for the drain stop lever, to screw or bolt the base of the faucet to the other, small wooden block.
In the case of my laundry room the sink is plastic and I was able to drill through it. The best way to secure your faucet depends on your specific situation.
Once the faucet is secure attach the supply hoses. Plumbers putty or plumbers tape applied to the threads of the faucet will help ensure that the connection does not leak.
Once you are satisfied with the connection turn on the water supply. Check all connections. Wipe the faucet dry and look for leaks. Watch the area over the next few days to spot any slow leaks or drips.