Photo by Roxanna Gonzalez
There is a free relationship/dating class online from BYU - it is geared more towards youth/first time daters, but there is some great info in it:
BYU Online - Dating: Romance and Reason
Here is the full list of FREE BYU ONLINE COURSES
The church (LDS Family Services) offers relationship classes for free, and I think there is a manual for it that is available for about $3.
The church website lists some great info for single adults as well as info on how to contact the closest office to find out about the classes:
LDS Family Services - For Single Adults
A listing of various singles dating sites, and resources for singles activities/leaders is at the LDS Section of About.Com
Utah LDS Singles Hotline: 1-800-537-6726
Singles Activities Websites (Utah):
Please add any other free or low-cost LDS Adult Singles resources YOU know about.