Ask Diego what you need to do to be accepted. He tells you to speak to Thorus, who stands outside the castle gate. Thorus sends you back to Diego. Diego says you must build up respect among the Shadows in order for him to recommend you to Thorus.
Diego
Diego's describes his respect task as a "Test of Faith": in this case, going to the Old Mine and safely bringing back a list of the supplies they need. He says you can get a map from Graham. To find Graham head west along the wall (i.e. face the castle gates and turn right) and you'll find him. He offers to sell you the map, but you should insist Diego said he'd give it to you. When he still refuses threaten him with violence, and then he'll give you the map. You can also buy maps of the Colony and the Old Camp from him which you may want to do. The maps are not annotated, but an arrow lets you see where you are and which way you are facing.
Whistler
This is a simple one. Whistler wants you to get a special sword Fisk made for him. Agree and he will give you 100 Ore for the job. Head on down the slope and talk to Fisk. He's the darker-skinned Shadow, and if this is your first time in the area he'll introduce himself to you when you reach him. Ask about the ornamental sword and agree to pay 110 Ore; if you don't have the extra 10 Ore on you just steal some, trade with Fisk for it or go back to Whistler and ask for it. Do not mention Whistler was only going to pay 100 Ore as this will result in Fisk refusing to sell it to you. While you're here you might want to buy a Digger's Discipline from Fisk. It delivers 20 damage and only requires 10 strength. Once you have the sword(s) head back up to Whistler and ask for the 10 Ore (if you didn't already) and then hand him his sword. He will be very pleased and promises to put in a good word for you.
Unless you are planning to rip him off, return the sword right away- otherwise after a few days he will become hostile to you and make this quest impossible to accomplish.
Sly
See Vanished Guard.
Fingers
Fingers is a thief. He wants you to demonstrate you have a thief's skills. Robbing every chest in the camp isn't what he's after, however; he wants you to take training and gain skill levels in the thief's arts. He can train you in Pickpocketing and Lockpicking. For Sneaking, however, you have to find the expert Cavalorn. His hut is in the canyon west of the old camp. Just follow the path and you should get there no trouble.
If you train in basic Lockpicking and Sneaking, Fingers will vote for you (learning Pickpocketing is optional). The trade-off for the skills is using 20 skill points to earn 100 experience.
Scatty
Scatty is the arena master. Find him by heading east along the lower level of the camp. In order for him to vote for you you must challenge Kharim.
You have two options here.
Let him beat you
Once you've challenged him drop your Ore on the ground (so he can't grab it off you) and then go into the arena. It shouldn't take him more than a couple of blows to fell you. He'll then check your body for Ore and leave you alone.
Beat him
You'll need some strength, armor and magic items if you hope to beat him. It's also possible to soften him up outside the ring. Just hit him a bit, then if he starts hurting you run away and come back. It takes a while for him to heal, and in this time you can challenge him and finish him off.
Regardless of what you do Scatty is impressed that you had the courage to challenge Kharim, plus he hates Kharim because he's from the New Camp.
Dexter
Dexter wants you to steal a recipe book from the Sect Camp. Doing this will also satisfy Fingers. Head to the Sect Camp. You can get Baal Pervez to lead you there if you want (he's over by the campfire just to the right of the gate). Once there take a hard left to the temple, then follow the far left path around. When you reach the weed distributor climb the ladders just past him and go into the hut with a bodyguard outside. Cor Kalom doesn't mind if you pick his chest open but his assistant does, so wait until he leaves. Once you have the recipe bring it to Dexter.
Thorus
See Thorus' Quest.