I'll warn you that making string blocks is addicting but if you're ready to begin we'll point you to Bonnie Hunter's Quiltville site where you'll find a String Quilting Primer to get you started.
If you plan to make blocks to mail in for HeartStrings group quilts PLEASE read the guidelines first as Bonnie's blocks are constructed with a few differences.
However, if your plan is to make the top and request it be quilted by a volunteer quilter or if you're making the entire quilt yourself then any method, any string pattern goes! This Basketweave Strings is one of my favorites from Bonnie's site.
Make sure you check out all the string quilt variations by clicking the links at the bottom of the String Quilting Primer page and you can find more string quilts and instructions on making them by clicking these links:
When you're ready for something a little more advanced, check out Bonnie's String Spiderweb