I am sure this question found its' way to my JustAsk mailbox because I am a specialist in Sign Language instruction. I own the company SIGNING FAMILIES™ (http://www.SigningFamilies.com). We create a variety of sign language learning tools and also offer workshops, classes, etc. We also have ONLINE ASL COURSES!
Depending on the age of the family member will determine at which level and what vocabulary you could start with. Feel free to send me directly details of your situation.
In the meantime, I applaud you for wishing to learn American Sign Language.
In addition, you can also check out the plethora of online dictionaries to help you with basic vocabulary. These online dictionaries include SigningSavvy.com and ASLUniversity.com
I found a website called ASLpro.com, they seem to have good video lessons to start you off on learning sign language.
When you arrive on the homepage, they do ask for a $5 donation, but this does not prevent you from entering the site. Also they're supposed to be a free resource, so other than the donation button, everything else should cost you nothing.