Sounds like a quilt I made out of scraps of fabric. At one point, I had over 200 different fabrics from all sorts of projects, so I just cut a square or two out of each and sewed them all together! Good use of scrap fabric.
As for fabrics, cotton weaves are best, but since it’s a scrap quilt, anything would probably do. If you’re buing fabrics, just go to the fabric store, go to the quilting cotton/calico section, and just pick out a bunch of fabrics you like and get like 1/4 yard of each (more or less depending on how many fabrics you get and how large the quilt will be).
It’s always a good idea to wash and dry your fabrics before sewing, to preshrink them.
Next, figure out how you want to cut the pieces. You could make a 4X4 template out of cardboard and just trace with a fabric pen and cut (you could do several layers, like 4 or 6 at a time, if you have good scissors). Or if you have a rotary cutter and cutting mat and clear quilters ruler, you could cut the squares out that way. It’s very quick and exact.
Next, sew 'em together. A 1/4 inch seam is standard. This makes it easy because you can just run the edge of your fabric along the presser foot, which is exactly 1/4 inch.
Here’s the order you would do it in. Let’s say you want to make a quilt that is 10 squares by 10 squares, so it would look like this:
XOXOXOXOXO
OXOXOXOXOX
XOXOXOXOXO
OXOXOXOXOX
XOXOXOXOXO
OXOXOXOXOX
XOXOXOXOXO
OXOXOXOXOX
XOXOXOXOXO
OXOXOXOXOX
(Obviously, IRL, your quilt would be square, not rectangular as in the above graphic.)
Start by taking a bunch of squares (Xs and Os) and sewing them together edge to edge in a line, forming a long strip. Make 10 strips that look like this:
XOXOXOXOXO
Pres all the seams in the same direction.
Then sew all of those long strips together lengthwise, making sure the seams match up. Always use pins, or else it will look sloppy and seams won’t match up.
Now, you have the quilt top. Choose a fabric for the back, cut it to size, sandwich cotton batting between the two layers, smooth out and pin together (use quilters safety pins) then tie it with yarn. Then, you’re ready to bind the edges, and you’re done!
I can tell you more about binding, but I have to leave now, but I will come back later.
Good luck! 