Some quilts just look best set on the diagonal. Some blocks, like basket blocks, really look silly set straight, or lying on the side. But it's not that hard to set a quilt on the diagonal, so don't panic.
Look at your quilt as being lopsided, set sideways. The rows run from corner to corner, rather than from left to right. The arrows point to the rows in this quilt.
On this quilt you can see the side triangles, or setting triangles, are in green.
The yellow triangle blocks in this quilt are the corners. The measurements for the corners are the easiest to figure, simply add one inch to the finished block measurement and cut two squares that size. Then cut those two squares in half diagonally, which will give you your four corners.
The quilt on the left is not put together, and you can easily see the rows. The first and final rows are sewn together with the setting triangles and corner triangles attached. The other rows are sewn together, but the setting triangles are not attached yet.
If I had a ten inch basket block, my corner blocks would be 11 inches. I would cut two, and then cut each one of those in half diagonally.
My corner blocks
The sides are a little harder to figure out, but fortunately a lot of people have done the math for us. Many quilt books give you formulas for figuring how to cut setting triangles blocks. I personally use the formula found in Trudie Hughes' Template Free Quiltmaking published by That Patchwork Place. She says that we should multiply the side measurement of our block by 1.414 and add 1 1/4 inches to that. (The extra 1 1/4 inches is for your seam allowances.)
If you have a ten inch block, you would multiply that by 1.414 which would give you 14.14 to which you add 1 1/4 (or 1.25) That equals 15.39, which is close enough to 15 1/2 that I would cut my side triangles 15 1/2 inches. Now, to assure that the stretchy side of that square is not on the outside of the quilt, you need to cut that 15 1/2 inch block in quarters diagonally.
My side triangles
A few more helpful tidbits-
The reason we cut the side triangles blocks in quarters is to assure that the bias edges are not on the outside. You want your quilt to lie nice and flat, and if you put stretchy edges on it, it probably wouldn't. By cutting the side blocks in quarters, you are putting the bias edges on the inside of the quilt. (Be sure to treat it accordingly when sewing with it, and don't pull it too much.)
The same thing applies to the corner blocks. By cutting them in half, the bias edge is on the inside of the quilt, and not in the corner where it might get stretched out of shape.
Also, I find it helpful to lay out my diagonal set quilts on the bed when I'm getting ready to sew the rows together. That way I can see how they go together. If it's a huge quilt, I will pin the blocks together into rows before I carry them to the machine, assuring that they stay in the order I want them to stay in.