How to Zoom in QGIS Print Composer Without a Scroll Wheel

I assume you're trying to zoom within the map frame, not zoom the composer itself (for which you use the magnifying glass buttons).

If you select the map frame and click the 'Item' tab, then the 'Extents' accordion, you can adjust the map extents. You can also use the 'Set to map canvas extent' to set it from the extents of the main QGIS window (roughly; if the canvas and the map frame have differing aspect ratios, the extents won't be exactly the same).

You can also use the 'Move Item Content' button, which looks like this:

This will allow you to move the map frames contents without needing to go back to the map window. You can also zoom in and out with the scroll wheel (which unfortunately you don't have).

You can change the scale by selecting the item tab and altering the scale numerically.

For people looking for this in QGIS 3: The answer of James S is basically still valid but the Icon of the "Move item Content" has changed in the mean time and looks now like this: (in this case with black background because I use a black theme in QGIS)