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The Coyotes - Starting the Investigation
You can get this quest by finding Captain Parker at the Aerotech Office Park. You can find this makeshift compound to the south of Freeside. It's a big square with a fairly small entrance, but it's not too far off of the main highway. Once you're inside, you can look for Captain Parker on one of the main benches. He usually sits outside during the day, and he seems to always report to the big tent to sleep.
As soon as you talk to Captain Parker, you should be able to get a few quests out of him to help out the refugees in the office park. It seems that a large number of people went missing after agreeing to work with some scavengers up in Westside. We should probably check it out.
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The Coyotes - The Investigation
The investigation is fairly simple, since we have a few people to directly investigate. Go to Westside and go to the Casa Madrid Apartments. You can either find Dermot and Saint James sitting outside and a bit to the left against the building, or they'll be in their rooms.
If you talk to them, you won't get much. Dermot won't say anything and all Saint James will do is act suspicious. Something's going on, but there aren't any ways to convince them to spill the beans. You need to investigate.
Go into the Casa Madrid and talk to Pretty Sarah by the stairway. She'll be able to tell you a little bit about them and mention that her best girl, Sweetie, does a whole lot of business with Saint James. She's got a room on the top floor, so just go up there and talk to her. You can bribe Sweetie to learn about Saint James' "unique" requests (it should be free with Lady Killer). This isn't technically necessary though, since you can get the same information by reading Dermot's ledger.
On that note, while you're here, you should slip into Dermot's room and grab the ledger off of his desk. I believe that it should be unlocked or at least very easy to pick. The ledger is in plain sight on the table. Read through it to learn that Dermot and Saint James were selling their refugee workers as slaves to the Fiends...and a whole lot more. For the other piece of evidence, go into Saint James' room on the bottom floor. If you can't pick the lock, you can just buy the key from Sweetie.
Go into Saint James room and take the stolen teddy bear off of his bed to tie him into it clearly (if nothing else, it gives you a better option to taunt him).
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The Coyotes - Justice
Your options from here are actually pretty straightforward. You can just go back to Captain Parker and report the evidence to him, although you can also choose to take justice into your own hands for a bigger reward. Walk up to Dermot and Saint James, preferably while they're resting outside (if you want to take them out together). Show Saint James the teddy bear to make him angry enough to attack you in the streets along with Dermot. Dermot's SMG shouldn't do more than scratch your armor, but Saint James' power fist has the potential to hurt you. Either take him down quick in melee or fall back a bit and shoot him in the head. Neither one of them is armored well, so it should be over quickly. If you do this outside, make sure that you watch your fire. You don't want to make the entire town go hostile.
Once they're dead, you can loot their bodies. While the Casa Madrid tentants may have some commentary, the only person that adds much to your quest is Pretty Sarah. If you talk to Marco, you can find out that she was burned badly by Cook-Cook in the past. Since Dermot and Saint James sold people to Cook-Cook, you can show Pretty Sarah the ledger and she'll change her tune immediately and give you four doses of Med-X as a reward.
Once you're ready, go back to Captain Parker and report your success. If you killed Saint James and Dermot, you'll tell him about their deaths first, but secure your innocence and your reward by presenting the evidence to him. Captain Parker should reward you with about 150 caps.