1. Open the .logo.ai. file with Illustrator.
2. Make sure the toolbox is visible. Select Window>Show Tools if it is not.
3. Adjust magnification as needed by using Zoom Tool from the toolbox.
4. Switch to Type Tool and replace "Company Name" with the name of your company.
5. The text you typed might happen to be shorter or longer than sample text. Use Selection Tool to position new text properly.
6. Since letters have changed, the underline also needs some editing. Select a portion of underline with Direct Selection Tool . In some cases other elements get selected instead of underline, send this element to background with Arrange>Send To Back from context menu.
7. Resize lines by dragging nodes with Direct Selection Tool. Holding down the Shift key allows preserving vertical coordinate of a node unchanged thus keeping the underline horizontal.
8. In case you need to remove extra fragments of underline select them and choose Edit>Clear.
9. To obtain additional fragments of the same width and color copy an existing fragment with Edit>Copy and then select Edit>Paste. A copy will appear to the upper left of initial line fragment. Drag the copy in place with Selection or Direct Selection Tool and resize it as described in substep 7.
10. When you have created appropriate number of fragments of underline and resized them as needed you may want to make sure they are all horizontal and leveled. Select all fragments with Direct Selection Tool by either drawing a box around the whole underline or shift-clicking each fragment. Right-click the selection and choose Average. Set the radio button to Horizontal position and click OK.

There is much more to Illustrator than this. http://graphicssoft.about.com/cs/illustratortuts/ is a good place to start improving your skills in order to make your logo really unique.