[D&D] How to give missions to player?

Storytelling games... well they are different. You don't necessarily do quests in those. I mean, while I write this I am watching Elder Scrolls: Oblivion gameplay from cloned TV screen and in computer games you run here and there, talk to people and you can find missions and quests everywhere. Someone has serious rat problem at their wine cellar, someone lost his wedding ring, someone is concerned about those orcs making a camp near the city border...

There is always something to do. Hard part is, that I and my player must get rid of this WoD-ish mindset and tune our mind into fantasy-roleplay-adventuring. If you go to pub, there is always this cloaked guy who has something interesting to say.
There are always raiding bandits or orcs troubling some city.
City well, yeah, poisoned.
Monsters in sewers? Yes, kill them and find out who is behind. And kill him too.
Seal of earth-thingie. And a rumour of a door with earth-thingie. Find the cave and the door inside. Combine. Profit (after killing monsters).
There is attempt of assasination to duke/king/merchant/cow and you must solve it/prevent it/commit it.

Or you couldn't give a shite about any of those quests and find new ones.

And play reporting from my D&D campaign.
Last time LuvMina and his halfling friend found out secret loot of guy who discuises as a beggar for reason unknown. Halfling Francis want's to know why is he doing that, but Luv is not interested.
Bummer. There could have some investigation thingies (actually, man wanted to get into thieves' guild and he had to steal x amount of gold to get in as an apprentice) but playercharacter doesn't care about it.
Ok, I remember that hey, she has now enough gold to do familiar and off she goes buing supplies. (insert here long conversation and lots of googling about how that familiar summoning/making actually goes. PHB only tells you buy 100gp worth of stuffz and spend a day doing it and you get it. We wanted to know what does familiar need. How does it manifests or comes by.) She went to Wizards street, bought snake scales, strange powders and stuff and found the Guild of Wizards. Decided to go and see what's it about.
Okay, now Luv wants to join a guild. But she is sorceress, not a wizard. But one fellow at guild told, that maybe LuvMina could join as an apprentice but she wouldn't benefit from her membership alot (she don't learn spells from reading and cram up on them and will propably not fit in). But she wants to see wizards and to belong in somewhere and become an adventurer (that's the reason she left home in the first hand anyways).
Okay, she meets the guy next day. But before it, some familiar summoning.
Mixing stuff and chanting and things all magical and snake squirms in.

This evening in game is that next day. We start game when LuvMina meets the dude from wizards' guild. And I am SO pleased. Perfect reason to give quests to character.
"So, you want to join our guild?"
"YESSIR!"
"You have to prove yourself."
"YESSIR!"
"First [insert quest here] then we'll see again."
"YESSIR!"

Continue that patter few times, 1-2 levels worth of experience. If you don't have a plot by then...