Open GarageBand and select "New Project" and "Songwriting" in the first dialog box that opens, then hit "Choose." Choose your song name and the location to save the file; if you do not know much about signature, or key, do not worry about these --- the default settings are fine to begin playing. Slide the "Tempo" bar up or down, depending on whether you want a fast-paced song or a slower one; this setting will noticeably affect your loops. For a first song, between 90 bpm and 160 bpm is probably best.
Click the button with an "i" inside a circle in the lower right corner to browse the variety of instruments available. To change one of the defaults, click the bar on the left that indicates that instrument, and then find and select the instrument with which you would like to replace it from the menus on the right.
Click the button next to the "i" that looks like an eye to begin choosing the loops you would like to use as "beats." Clicking one or a selection of the oblong buttons in the top right will then give you a menu of loops that offer similar qualities or are intended for that type of instrument. If you select a loop with a green box, you will be able to edit the loop, to make "beats" exactly as you want them. Blue-box instruments are recordings (and as such allow only limited editing --- namely, deleting parts of the loop).
Select the bar of the instrument where you would like to place the loop you have chosen. Click and drag the menu-bar item of the loop onto the instrument's bar to where you would like it to start, to make one repeat of the loop. At the top of the space where loops are is a ruler indicating "measures" of the song, which can help you choose where to place the loop. If you would like the loop to repeat more than once, hold your mouse over the top right corner until it changes to a small looping arrow. Click and drag the loop out to however many repeats you would like.
Repeat this loop selection and placement for the other instruments. You can also use multiple loops for one instrument at different times; place the new loop to the right of the old one to make it pick up where the first left off. Use the playback controls at the bottom of the window, between the round "Record" button and the timing window, to listen to your work.
Record your own voice by selecting the "Voice" bar in the top left of the list of instruments. Put on your headphones so you can hear the other instruments without them interfering in the recording. Make sure the recording starts at your desired location by clicking and dragging the triangle in the "Measures" ruler attached to the red line to where you would like your voice to come in. Hit "Record" and sing a few bars. Go back and listen to the recording. If you are too quiet or too distorted, you can adjust the recording level of the microphone by selecting the "i" button in the lower right, and a "Recording Level" bar appears below the list of instruments.