I went to Riften and met Mjoll, She so far has not offered me any quests though I know she does have one to give and that she will become your follower after you complete it...Can anyone tell me how or what to do to get her to give me the quest needed to make her a follower??

Friend, fill me in will you (I'm not too bright)...
What does this have to do with the Dragonborn DLC?

Anyway, Mjoll has lost her beloved enchanted glass sword and needs you to get it back for her.
(She almost died when she lost it, and apparently Aerin saved her, for which she is eternally grateful.)
I think perhaps you need to reach a certain level or something, before she asks you...

And I noticed the Unofficial Skyrim Patch identified an issue where Beth made a mistake giving her that sword.
She is heavy armor / two-handed all the way (typical Nord) but Beth made her sword one-handed.
I retrieved the sword for her, but now I see she patrols Riften with a big two-handed version of it!
(Which is not what I retrieved... so it's kinda freaky)