You are going to need something to cut on. I use an 18"x24" Omnigrid Gridded Mat. Why this one? Because this is the one my parents bought me for my birthday 6 years ago. Wish I had a better answer.
You will also need something to cut with. I use an OFLA rotary cutter. Why this one? Again, because this is what my parents bought me. If you really don't want to spend the $11, because you think you'll never use them again, you could just use scissors I guess, but I think it'd be harder to ensure your cuts were straight. Plus, if you own a sewing machine (and how else were you planning on sewing this big boy together?), I'm pretty sure you will find this rotary cutter useful at least now and again!
You'll also want some kind of straight edge with a ruler on it. Again, if you aren't a big sewer/quilter outside of this project, you could just use a regular old ruler, but I would honestly have hated to cut out all of my t-shirts using just a ruler. (I think it would have taken much longer and not been as accurate.) I just use a 6"x12" Omnigrid Quilter's ruler. Why this one? See my answers above. (So, by now you can guess that I mentioned to my parents that I wanted to learn to quilt, and for my 26th birthday they hooked me UP with quilting supplies!)
I also have handy a good pair of fabric scissors (I have a pair of Fiskars I really like).
And of course if you are new to t-shirt quilting, I highly recommend a copy of "How to Make a Too Cool T-shirt Quilt" by Andrea Funk (ebook $15), since she gives a unique explanation of how to actually piece the quilts together.
However, if you just want to do big fat squares like this, any ol' quilting tutorial will do. You can go buy/rent a book on quilting basics, or find dozens of free ones online: Like this one or this one.
Here is a good list of basic quilting supplies, which include more information on the supplies I've listed here, and some additional basics that you might want/need (especially if you want to do other quilting projects in the future).
Next: Cut Out T-shirts