You can't learn how to use Lightroom without learning how to use the Develop module. This is where you edit your photos, and will likely spend the majority of your time. The Develop module is made up of a bank of tiered sliders that are organized into several adjustment palettes. Click on a category like Basic, and you will be greeted with a variety of basic image adjustments like white balance, exposure, brightness, contrast, saturation, and so forth. Simply move the slider of your choice to apply an adjustment to your image. To make further adjustments, click on another adjustment palette like Tone Curve, or Effects, and continue to shape your image the way you want it.
One useful tip for working with the adjustment palettes is to turn on solo mode. Without this, every palette you open will remain open until you close it. With solo mode activated, when you move from one palette to another, the one you were previously working on will automatically close. To do this, right click (PC) or Command click (Mac) on one of the palettes and select solo mode. This will save you a whole lot of vertical scrolling.
It is important to note that Lightroom 3, like Aperture and Capture One, is a non-destructive image editor. This means that your original photo will not be altered in any way. Think of your adjustments as a layer of data that sits on top of your original photo to make it look the way you have decided it should look. Your changes are not permanent, and can only be seen outside of Lightroom if you export images from the Library module. In this way, if you decide to re-edit the photo a different way, six months or a year later, you still have the original photo to work with.