Basting a quilt is when you sandwich the quilt in three layers: the quilt top, batting and the backing. You need to baste these three layers together before doing the actual quilting. Here's how to do it, 4 steps below!
Update (added 5/02/11) - I also added a basting alternative at the end of this tutorial, which explains how to baste without using pins. The method is spray basting. I've tried it before and would recommend it, especially for bigger quilts.
Step 1 - On a flat surface, lay your backing fabric flat on the floor with the right side facing down (the wrong side of the fabric will be facing you). Flatten out any bumps as best as you can (tip: it helps to use a yardstick or your 6"x23" rotary ruler to help smooth out bumps). Tape the corners and sides as needed so that the fabric doesn't shift around on the floor; I recommend using painter's tape. The backing fabric should always be at least 2-3" bigger around the perimeter than the quilt top.
Step 2 -Next, lay your batting on top of the backing fabric. Flatten out any bumps as best as you can. (Tip: I suggest using Warm & White cotton batting or Soft & Bright polyester batting. Both are made by "The Warm Company" and have almost a fleece-like feel to them, making them much easier to work with (i.e. you don't have to deal with uneven batting that bunches while you're machine quilting). However, if you are working with a fluffier batting, throw it in the dryer for ~10 minutes to help un-wrinkle it).
Step 3 - Next, lay your quilt-top on top of the batting. The right side of the quilt top should be facing you (the wrong side should be facing the batting). Make sure the quilt top is centered on the batting. Flatten out any bumps as best as you can.
At this point, your quilt should be layered as shown below with the batting sandwiched in between the quilt top and backing fabric. This is called a quilt sandwich.
Step 4 - Now, you need to pin all three layers together to keep them in place so that they don't shift around later while you're quilting. I recommend using curved safety pins, as shown below. The curve in the pin helps immensely when trying to pin through all three layers on a flat surface. Pin every 5-8 inches.
Start pinning on one end of the quilt. Remove the tape on one end, and start pinning every 5-8 inches. As shown below, roll the pinned quilt upward as you go for easier pinning access.
That's pretty much it. Let me know if you have any questions!
Basting Alternative - Spray Basting (no pins needed!)
I typically use pins (as explained above) to baste my smaller quilts; however, for the larger ones I would recommend spray basting them. Below are two video tutorials I found on YouTube that explain pretty well how to spray baste. In these videos, the gal spray bastes them by pinning the quilt layers to a wall so that all layers three layers drape evenly over one another.
However, you can also spray baste on the floor (which is what I've done in the past). You just have to get down on all fours to make sure the layers are smoothed out evenly; it still helps to tape the backing fabric to the floor as described in step 1 above. Similar to the video tutorials, be sure to line your floors with newspaper around the quilt so you don't get sticky floors.
I recommend you watch this video first. Fast forward it to minute 6:15.
For more details on spray basting on a wall, you can watch this supplemental video:
You can likely find spray basting glue at your local quilt shop or crafting chain store. Below is the brand (Tailor) that I've used. I've also heard the brand 505 is very good.
Hope this tid bit helps. It's always nice having some options. :)