Apple Loops
After you click on New Music Project, you will see a screen that looks like this:

Select a tempo and key for your song (you can always change this later) and click Create. Now you will see a window with a track that uses the Grand Piano Software Instrument (ignore this for now). In the lower left-hand corner, you will see a button that looks like an eye--this is the Loop Browser button. Click on it to see the different categories of loops.

Selecting a Loop
Click on a category and you will see a list of loops on the right. If you click two categories at once, the list will only include loops that match the criteria for both selected categories. By clicking Reset, the categories will be deselected. To listen to a loop, simply select it. Once you find a loop that you like, click and drag the loop to the timeline directly under the Grand Piano track. A new track with your loop will appear.
Looping the Loops
Now you can add as many tracks with different loops to your song as you'd like. To listen to your first loop while you are trying out other sounds, you can click on the Cycle button (the button with two arrows making a circle) or you can stretch the loop out and push play (position the cursor in the upper right-hand corner of your loop until you see an arrow and click and drag to the right).
Editing
You can edit your song by moving the loops around, shortening and lengthening them, and changing the overall tempo (do this by clicking Temp and moving the slider around). To make editing easier, you might want to zoom out to see your entire song. You can do this by moving the zoom slider below the track headers (left-hand side above the loop browser).
Here is an example of what your song might look like:

Adjusting the Volume and Panning in your Song
Once you have arranged your loops the way you like them, you might want to adjust the volume and panning. You can adjust these parameters for your entire song, or for each individual track.

Click Play to listen to your song. You can set the track volume sliders and pan controls of each track to your liking, OR, if you'd like these parameters to change over time, click the triangle in a track header to reveal the track volume/pan curves. Then, click the volume/pan curve to create an insertion point and drag the curve up or down to change the volume/panning over time. Similarly, to change the volume/panning of your entire song, you can adjust the curves for the master track. To show the master track go to Track menu > Show Master Track.

Advanced Editing
You can also change the pitch during your song by moving the pitch curve around on the Master Track. Dragging the curve up to +7, for example, will raise the pitch a 5th. To add effects to your song such as echo and reverb, change the master track's settings in the Track Info pane (select the Master Track and then click the "i" button on the bottom right-hand side).
Locking a track
If you feel like you won't make any more changes to a particular track, you can lock it by clicking the lock icon in the track heading. This will prevent unintended changes to your track and reduce the processing power required to play back your track. If you want to make changes you can always unlock the track.