You're going to have to complete two contracts for Azzan in Anvil and one contract for Burz gro-Khash in Chedinhal, but it doesn't matter where you start. You can do the two and then the one, do the one and then the two or split the difference. You'll receive a promotion after completing your first contract and then another when you've completed the next two.
A Rat Problem:
You'll start getting hints about this contract as soon as you join. Seems like almost everyone will have a Rumor to the effect of "Why is it always rats for the new members?"
You're sent to Arvena Thelas about a rat problem. Unlike your first mission in Morrowind, you don't need to exterminate the rats; you need to protect them from the starving mountain lion in the basement. Seems Arvena keeps them as pets. So off you go to the basement to take care of the Mountain Lion. After you report back to Arvena, she's worried that there might be more around, and sends you off to find Penarus Inventius (he's a trainer in Marksman if you're looking for one). I've always found him at his house, but his schedule does have him running around in the wilderness for a bit. He's not hard to find, though.
Once you find him, he'll suggest a hunt. Your destination is in a clump of rocks a bit northwest of the Anvil city gate where you'll find four more Mountain Lions. It's OK to run ahead and deal with them on your own, but if you're still relatively low level, you might appreciate the help that Penarus can give. Once they're dead, you can go back to Arvena.
Arvena sends you back to the basement where another Mountain Lion has managed to get in. Take care of it and then go back to Arvena again. By this point, she's certain that her neighbor, Quill-Weave, is behind the problem and wants you to spy on her. Rather than confronting Quill-Weave directly (she'll deny any involvement), stand near the brick wall to the east of Arvena's house and stealth yourself (you may need to hide completely if your Stealth skill isn't that hot). About dusk/dark, Quill-Weave will sneak into Arvena's back yard and drop a piece of meat on the ground. She won't do this if she can see you, which is why I suggested hiding completely if your Stealth isn't up to the job. You'll get a journal entry when she does this.
Confront her about it and she'll confess to dropping the meat to lure the rats out of the basement where she hoped that the town guards would deal with them. She didn't plan on the mountain lions. She'll offer some Acrobatics training if you'll keep quiet about her role in the whole thing. When you talk to Arvena afterward, you can either keep Quill-Weave out of it (you'll get 300 gold and can pick up your Acrobatics points from Quill-Weave later) or you can tell about what she did and get 300 gold and a couple of points of Speechcraft from Arvena.
Surprisingly, you do not need to report back to Azzan to let him know that you've completed the contract, although you should go back to him to talk about "Advancement". You can pick up the second contract now or wait until later. (back to top)
The Unfortunate Shopkeeper
Azzan sends you off to talk to Norbert Lelles over at "Lelles' Quality Mercandise" in the docks section. Someone has been breaking into his store. When you talk to him, you'll find that your job is going to be to guard the store while he heads off to the Flowing Bowl next door until the problem is solved. You're to stay there until the thieves show up.
The thieves (there are three of them) will show up sometime after 11pm, but before 4am. Individually, none of them is any great shakes. However if you don't position yourself so that they can only get at you one at a time, they can and do gang up on you, which can be anywhere from painful to deadly.
When the three thieves are taken care of, head for the Flowing Bowl to let Lelles know and collect your contract fee. It turns out that all three of the thieves are former employees, which might explain how they were able to get in. Don't forget to pick up their equipment. You can sell it to Lelles once he's back in business (it might take a bit for the bodies to disappear, though).
Azzan has no more contracts for you and sends you off to Burz gro-Khash in Cheydinhal. (back to top)
The Desolate Mine
Burz gro-Khash sounds like a drill sergeant. He needs you to deliver some weapons to fellow Guild members at Desolate Mine (which will be marked on your map).
When you get to the mine, speak to Rienna (who will take the bow). Give the Orc the hammer and the sword to Elidor and then the three of them (with you hopefully following) will head off to kill all of the Goblins in the mine. Once that's done, you can go back to Cheydinhal to collect your fee. Note that you will be docked a percentage of the contract fee for each of the guildmembers that dies (and using the console to resurrect the dead ones won't change that), so be as helpful as you can, even if it means just playing field medic for the others.
The mine isn't that big (only one level), but it does twist and turn a bit and your guildmates have a nasty habit of getting in the way when you want to beat on something. Be careful. One or two "friendly fire" hits won't cause them to attack you, but since the Goblins are going to be trying to kill them, you'll just be making the Goblins' job easier and yours harder.
Assuming that you have completed Azzan's two contracts, when you report back to collect your fee, you can ask for advancement to Journeyman and will be sent off to talk to Vilena Donton in Chorrol about doing duties for the guild.