BE AWARE, there might be some spoilers here.

I just wonder how I become Thane of Riften ? I am no fan of the Thieves Guild and have decided to avoid them, so in order to becoming Thane of Riften I went for that quest that leads you to aid the Jarl in destroying a bunch of Skooma smugglers.

So now I am confused;

I finished the quest by telling the Jarl the Skooma dealers are dead in that cavern, she then thanks me, gives me a reward but I do not see any '' Is there anything else you need my Jarl ? '' speech option which you normally would get for the miscellaneous quest for becoming Thane.

Is there something else I need to do before I can start the Thane quest?

yeah you gotta do some quests around town i think, just help some folks and a new conversation should pop up

The Thane quests are not specifically given by the Jarl, you just do some quests for the Towns people and when you have done 2-3 a conversation topic should appear with the Jarl that gets you the Thanehood or whatever its classed as being the Thane lol

Thanks, I'll give it a try soon.

I was confused too. But I kept doing quests for the townfolk and then all of a sudden, a quest popped up that said "Talk to the Jarl of Riften" then when I spoke to her, she made me Thane.

Check with her Steward, too, but maybe you've already done quests for her Steward and that's why the Jarl gave you the Skooma dealer quest. I must've done the quests for the people of The Rift first and then gone to the Jarl for the Skooma one.