Summarize the following:
Do you remember any of her family members' names? If so, they may be on Facebook. This is especially true of younger relatives. Look through their friend lists. If she's on Facebook, it's likely she will be friends with her family members. Again, remember that the name's rarity has to be factored in. If she was named Jane, but her brother was named Tobias, you may have more luck trying to find him because of his name's rarity. Also, men don't change their last names through marriage usually, so searching for her father or brother or other male relatives is a good bet. Can you find any of these? If so, you could add them and ask them if they know about her. See if you have mutual friends with her. Facebook has a "mutual friends" feature that Facebook uses to match you with a name. If you have any mutual friends at all, she will be high on the list. Look on the right column under the feature "people you may know" and see if she comes up (she may if you have a mutual friend). Or you could just scour their friend lists to see if she's listed on them. This will work better if you knew her recently because it will be more likely she is still in touch with them. Do you know any details about her? Where she went to school or where she worked? If so, it may be worthwhile finding the school or company on Facebook. These people might know her. You also might find that she is already a member of the school alumni group or has posted on comments on it. You might be able to jog your memory of her family members' names or friends' names by looking at alumni groups or high school yearbooks (many are also scanned in online).
Look up her family members' sites on Facebook. Look up her friends on Facebook. Look up school alumni groups.