I piece curves using a regular sewing foot, not my walking foot. I pin A LOT. Sometimes using a stiletto to guide the fabric helps the curve be smoother, since you have a little more control. Actually, my "stiletto" is a bamboo barbecue skewer.
The concave curve needs to be clipped (about 1/8" or so) and sew with the concave curve on top. This prevents a lot of problems with tucks and puckers.
If you've got a kit with little room for error, I'd try making some curved pieces out of scraps and practice on them first.