Sewing with woven fabrics requires a little extra work because they fray much easier than regular cotton fabrics.
a) You can pre-wash your fabrics to help limit the fraying and shrinkage before you sew your porjects.
b) You can startch your fabrics as you iron them. This will act as a glue and reduce the amount of fraying while you are sewing.

My personal preferred method if starching. You can get starch spray at Walmart (its not expensive!)