I started this project last year after being asked to create a similar project for Dana. I had hoped to finish it in time for The Celluloid Jam 2 con, but that didn't happen. I've pecked away at it for a year, but most people could probably make one in a couple weekends.
Some of the shirts were from conventions I attended (and didn't get to). Some were from other casts I've visited (and plan to visit). And some were from Stage Productions. One was actually my own creation.
T-shirt quilts are as simple as any other quilt, with one extra step. You'll need to stabilize the back of the t-shirt pieces before cutting them out. This will prevent them from stretching into wonky shapes when you work with them. You can use any light-weight fusible interfacing of your choice - it comes in black or white, and you can also buy it with grid lines (not really necessary).
After applying the interfacing you can line up your t-shirt pattern to be cut. There are square rulers just for this purpose, but you can create your own template or even just measure really carefully. The benefit of the square ruler is you can see your design right through it when you position it - just mind your fingers if you're going to use a rotary cutter!
My quilt is 20 squares (4 x 5) with a border. It makes a nice individual lap quilt. You can add a border to get a little more room out of it (like I did), and you can also add sashing which are strips of fabric between each shirt square (not pictured). All quilts have a binding (red on my quilt).
The first part of a quilt is the topper - that's the layer with all your t-shirts sewn together. 1/4" seam allowance is all you need.
Once your topper is finished it's ready to become part of the quilt sandwich - the top layer, a back layer, and some quilt batting in between. Quilt batting comes in different thicknesses (lofts) but I wouldn't get too carried away if this is your first quilt. The iron-on battings are particularly handing and will keep your sandwich from shifting around while you work on it. Or you can use fabric spray-glue like I do.
The next big step is actually quilting it. Stitchings that run throughout the quilt to permanently hold it together. The stitches can be random or planned. They can go around edges (stitching in the ditch) or right through your squares. Most batting packages will recommend that stitches be no more than 8" apart.
When you're done quilting you can trim your edges carefully (any excess batting and back fabric) and apply your binding. You can buy packages of extra-wide bias tape or quilt binding for this, or you can make your own by cutting 1-3/4" wide bias strips very carefully (must be absolutely straight and on the bias!) I've known people who cut their own quilt binding on the straight grain with good results, but it's much less forgiving.