Step 1. Create your text in Illustrator. This is font is Bahaus 93.
Step 2. Expand the text. (Object > Expand, click OK.) This turns it into an object. Now you can fill it with a gradient by clicking on a gradient swatch in the swatches palette. If you want, you can change the angle of the gradient by using the gradient tool in the tool box (Click and drag the tool the direction you want the gradient to flow) or by typing in an angle in the gradient palette. Of course, you can adjust the colors in the gradient just like any filled object by moving the distribution diamonds on the top of the gradient ramp preview window, or by adjusting the gradient stops at the bottom of the gradient ramp preview window.
If you prefer, you can also use the Create Outlines method: After typing your text, click the selection tool to get a bounding box on the text, then go to Type > Create Outlines, and fill the text with a gradient as above.
If you want to use different fills in the letters, you will need to ungroup the text first (Object > Ungroup) or select them separately with the direct selection tool.