After I met Delphine at Sleeping Giant Inn, she then waited for me at the entrance of Riverwood to continue the dragon-slaying quest. After going through the dialogue w/her, she wouldn't follow me. I used all the dialogue paths. I then fast traveled to the dragon grave hoping she'd appear there, but she didn't. So I fast traveled back to Riverwood to find she wasn't at the entrance. What should I do?

Are you playing on PC, by any chance? If you are, you can either try teleporting her to your location or advancing the quest through the console.

You can find all that stuff here relatively easily. Just look for the code, then go to the page that has her ID (probably her wiki page). To advance the quest line, go to the page for that quest. It may also be easier to search your topic in Google, as I'm sure others have had this issue.

no, i'm playing the xbox version, but thanks for suggestion