The first step in curved piecing is to put a fresh sharp needle in your machine.... choose a Microtex, size 70/10 you want a fine needle to minimize needle holes in your fabric.
My fabric is cut in assorted strip sizes from fat quarters, some are a little longer than others.
Align the straight inch of the strip set and sew the first inch of the seam - stop with needle down - adjust the strips as the edges start to curve, keeping the raw edges together - sew another inch or so until the edges are not aligned. Stop with needle down, realign edges, and continue to sew. Do this in very small increments - sew, adjust, sew, etc. until you reach the end of the strip set. I didn't say it would be fast, did I?
Once you finish the seam, check to make sure you have that fabric caught the whole way along - and don't ask me how I know that it's important to check.... trust me, it is!
Now press seam allowances to the 'dark side' and lay all the pieces out on the table while you celebrate!
I did some postcards with mine.... with an OCEAN theme!