It's easier than you think!
This instructable describes the basic concept of how to build a 36 spoke bike wheel. Experienced wheel builders will see certain steps omitted. This is by design in an effort to simplify the process for the first time builder.
We are also assuming, and this is a Herculean assumption, that you know the proper spoke length for your application.
That said, let's get started!

Step 1: Tools, Materials and Jargon

Tools
1ea. Spoke Wrench
Materials
1ea. 36 hole rim
1ea. 36 hole hub
36ea. spokes
36ea. spoke nipples
Jargon
Rim - The big hoop with holes around the edge
Hub - The thing in the middle that holds the axle and has 2 flanges on it with holes in them.
Spokes - The wire things with a bent nail-head at one end and threads at the other.
Wheel - What you get when you put all of these things together.
Port - Sweet red wine or the left side of the bike when facing forward.

Step 2: Examine the Hub and Load Spokes

The hub has flanges on it that are drilled to accept the spokes. A 36 hole wheel hub has 18 holes on each flange. Some hubs have every other hole countersunk to accommodate the spoke head. This one doesn't, so we can go right to loading our first set of spokes.
Holding the hub with one flange parallel to the ground, take 9 spokes and drop one in to every other hole of the flange. Be sure to load spokes from the outside edge of the flange for this first step. It will become apparent later why the direction is important.

Step 3: Examine the Rim and Begin Spoking

Look at the rim. Notice that on this one there is a ridge down the center around the entire circumference. Closer examination shows that the holes for the spoke nipples are slightly off center. Holes located closer to the port side of the rim should hold spokes that go to the port side of the hub.
Locate the valve stem hole. It's the big one. Beginning at the spoke hole next to the valve stem, insert a spoke nipple and thread it 3 turns onto the first spoke. Skip three holes, insert another nipple into the fourth hole and thread it three turns onto the next spoke. It's very important to thread the nipples onto each spoke the same number of turns. This will make for less work later, when we're truing the wheel.
Continue around the wheel, skipping three holes and installing the next spoke in the fourth until all nine spokes are in place.
If you did this right, holding the rim and letting the hub hang should look neat and even. If you skipped the wrong number of holes or accidentally grabbed the wrong spoke, it will be apparent. If this happens, just undo the offending spoke and move it to the right hole.

Step 4: Center the Hub

Grab the hub and rotate it clockwise until all of the nipples seat in their holes. They tend to hang up a little on the edges. Once they are all seated, the hub should appear to be in the center of the wheel and the spokes will slanted to the left. With the side of the hub that you just spoked facing up, insert one spoke from the bottom (inside) of the flange. This spoke is going to hold things in place while we load the next course of spokes.
This part is easy to get confused so follow along closely.

Locate the spoke you just installed (from the under side of the flange). We'll call it the locater spoke.
Look at the spoke in the next hole in the hub (clockwise).
Follow that spoke to the rim.
Count nine holes clockwise along the rim.
Install the locater spoke in the ninth hole.

This locator spoke should cross over three of the spokes form the first course. This spoking pattern is call Three-Cross. There are other patterns too, like Two-Cross, Four-Cross and Radial. Beyond that there is Lacing. Lacing is a technique where the spokes are weaved in between the spokes they cross over. I didn't lace this wheel because these are very heavy gauge spokes and difficult to flex (which is required to do this weaving). The most common method of spoking wheels is Three-Cross Lacing.

Now you should have ten spokes in the wheel and the hub should be roughly centered in it. It's all floppy right now, but things will tighten up as we progress.

Step 5: Load the Other Side

Flip the wheel over and load 9 spokes from the outside edge of the hub.
Take one of the spokes and hold it so it is pointing straight out from the center of the hub roughly parallel to all the other spokes. Slant it anti-clockwise and find the hole in the rim it best lines up with. This hole will be right next to one of the spokes from the first course of spokes.
Continue around the wheel installing each (next) spoke into every fourth hole as we did in the first course.
Now we should have 19 spokes in the wheel. Nine loaded from the outside of the hub on each side and one loaded from the inside of the hub (the locator spoke) on one side.

Step 6: Load the Inside Spokes

Next, take the side of the wheel with the locator spoke in it and face it away from you. From the inside of the flange, load 8 more spokes into that side of the wheel.
Just as in the previous two courses, install one spoke into every fourth hole around the rim.
We're almost done. At the end of this step you should have 27 spokes installed.
9 loaded from the outside of the hub on the port side of the wheel.
9 loaded from the inside of the hub on the port side of the wheel.
9 loaded from the outside of the hub on the other side of the wheel.
There should be no empty holes on the port side flange of the hub and every other hole should be empty on the other side of the hub.

Step 7: The Final Nine

All that remains to this assembly is to load the last nine spokes from the inside of the hub. Take any one of these spokes and cross it over three of the spokes that were loaded from the outside of the hub and it will be very near a hole. Install a nipple into that hole and continue around the rim as we did in the previous three courses.
When you're done with this the only empty hole should be the valve stem hole and all 36 spokes should be installed. If you followed the advice at the beginning and tightened the nipples 3 turns each, the wheel will be fairly straight even though it's still pretty loose and floppy.

Step 8: Tighten It Up!

This is the last step to building your wheel.
Starting at the valve stem hole, go around the wheel tightening each nipple ½ turn. This will take many trips around the wheel before the wheel begins to get stiffer. Be patient and you will be rewarded with a round wheel that will be true. Be impatient by over tightening spokes to get rid of the slop quickly and you will be punished with a wheel that is oval, out of balance and difficult to true.
When the spokes are tight enough, they will twang like a guitar string. There is actually a recommended amount of torque (apx. 30 in.lb.) for spokes, but who among us owns a spoke torque wrench?
Once all the spokes are tight, spin the wheel. It should spin freely and feel smooth.

Step 9: True the Wheel

True the wheel by adjusting spoke tension in areas where there are wobbles. You'll need some sort of fixture. It can be an old fork, your bike or a professional truing stand.
Place the wheel into the truing stand and give it a spin. There will likely be some areas where it wobbles to one side or the other. On the truing stand below there is a special gauge that you place next to the rim. This gauge lets you see specifically where on the rim and how much misalignment there is.
If the rim wobbles to the right, find the spot where the wobble is greatest and tighten one spoke on the left ¼ turn. If that doesn't straighten it out, loosen the two spokes next to it (they go to the right side) 1/8 turn. If the wobble is on the right, switch sides and follow the same process.
Make one adjustment and look at the whole wheel. If another area needs adjustment too, move to that area next. Continue adjusting different areas on the wheel until all the areas in need have been adjusted then go back and begin again.
The reason we do this one area at a time is because any adjustment you make on one side of the wheel affects the other side too.
When you're done the wheel should spin true and smoothly.
It's also a good idea to recheck your spokes after the first ride and periodically to see if they might have loosened up or stretched.