This tutorial will show you how to create color beacons in Minecraft for the PC.
In the name of brevity, I'll assume you're either in Creative Mode, or have crafted your Beacon(s) and have at least 9 resource blocks of:

Iron
Gold
Diamond
Emerald

In addition, at least one block of:

Stained glass of your choice (pane or block)

Before we begin, I'll give you a quick recap of your basic Beacon...

Step 1: Beacon Basics

Here we see a few examples of beacons on various sized pyramids. They may range upwards from one tile high, but for the purpose of this tutorial, we'll be using the humble 1 x 3 x 3 tile beacon.

Got that? Okay, let's go! :D

Step 2: The 9 Tile Beacon Pyramid

Here's your basic 9-tile Beacon.

It may be made with any combination of Iron, Gold, Diamond, or Emerald resource blocks. (The cheapest and quickest way to make a short pyramid in survival mode is with Iron blocks.)

No other blocks can make a Beacon shine. This includes blocks like Lapis Lazuli and Pumpkins.

Simply place your resource blocks in a 3 x 3 formation, as shown in examples. Once you're done with the resource blocks, place your Beacon block over the center tile.

Your new Beacon should now be beaming a giant bright laser in the sky.

Step 3: Boring Beacons Begone!

Now that you have all that taken care of, equip your block or pane of Stained glass.

Press Shift + Right-Click on the top part of the Beacon to place your Stained glass. (Otherwise, if you click on the Beacon without holding down Shift, you'll bring up the Beacon's GUI.)

Your Beacon should now have a color beam!

Step 4: Look at All the Colors, Man!

Here you see the basic Beacon colors you can get with just a single Stained glass block or pane.

Not impressed yet? You can make your own colors!

Step 5: Color Mixing With Stained Glass

Color mixing is simple if you know your basic color theory.

If you're unfamiliar with basic color mixing, the basics are:

Primary colors: Red, Yellow, Blue

Secondary colors: Purple (from Red+Blue), Orange (from Red+Yellow), Green (from Blue+Yellow)

If you have say, a blue block and place a red block over it, the resulting beam will look purple. If you placed a white block over those two, you would get a light purple. If you place a black block instead, you would get a darker shade of purple.

From my experience, it's better to use Red/Yellow/Blue color mixing than Red/Green/Blue...as you can see in the example, the R/Y/B color mix is much brighter and more visible.

[NOTE i: Plain glass will not change the color of the Beacon. White will also not change it unless it's combined with another color.]

[NOTE ii: Once you have a glass block over the Beacon, you don't have to Shift+Click, just build as you normally do.]

Step 6: Have Fun! :D

Now that you know how to make color Beacons, you can use them in many applications, whether it's to distinguish landmarks, power-ups, or just for fun!