its tricky becoming thane sometimes, i became thane in riften and wasn't even trying lol, i just got lucky with the right quests..you need to do the quest with the dark elf lady at the docks...and apart from that, sometimes there are other quests you need to do..my favorite place to live is markarth and i've bought the house twice and its a bit tricky, generally all you need to do is 2 quests but to get the right dialogue, sometimes you need to do other quests helping people...so there's specific quests you need to do, usually just one or two, then sometimes, and it may be random, you need another quest, generaly just a small type of helping someone and then it triggers the dialogue..i have it down pretty good for markarth but not riften.