Please note that this guide is only about obtaining money. In an effort to minimise spoilers, the guide does NOT discuss:

• the potential consequences involved; and
  
• when / how to spend the cash.

The guide is a work in progress: If there's anything I missed, just let me know in the comments section, and I'll make sure it gets updated.

Enjoy!

Scene One
Description: Fiona will be walking down an alley, and come across two Lil’ Psychos stabbing a man.
Action: Investigate, and you’ll have the choice of taking the dying man’s money, or returning it. Take it, obviously.

Scene Two:
Description: Fiona will be searching for a vent to gain access into a building. There'll be a bunch of faded posters, and a large toolbox.
Action: There are TWO cash stashes here. One is behind the Mad Moxxi poster – the cash will fall to the ground after she pulls the poster off the wall. The other is in a loot container to the far right of the screen. It’s surprisingly easy to miss.

Scene One:
Description: Fiona finds General Pollux.
Action: Mouse over the general’s coat pockets (below his medals), and you'll have the chance to take his money.

Scene Two:
Description: Fiona enters a garage, looking for repairs.
Action: There’s a loot container next to the vending machine. Use it (once you’re done exploring).

Scene Three:
Description: Shortly after entering the garage, someone will pitch a sponsorship deal to Fiona.
Action: Pick the “Sweeten the Deal” dialogue option, then the [Sell Out] action.

Scene Four:
Description: Fiona and Sasha are restocking.
Action: There’s some cash in a storage crate. Don’t worry too much about this one: it’s actually impossible to miss it.

Scene Five:
Description: Near the end of the chapter, Rhys has to decide whether to trust Fiona’s plan, or someone else’s. It's a pretty conspicuous scene; you'll know it when you see it.
Action: Trust Fiona (if you want the cash). You won't get the money just yet, but the decision will dramatically change the start of episode three.

Scene One:
Description: (You picked Fiona’s plan at the end of Episode 2, right?) Early on, she’ll be ducking behind crates in order to sneak up on an armed mercenary.
Action: Take out the merc, and pick up the money from the ground. If you’re too slow, something else will intervene, and you won’t get the money.

Scene Two:
Description: Shortly after entering ‘The Dome’ interior, player control will swap from Rhys to Fiona. Once inside, everyone will be standing around talking, etc.
Action: Open the loot container – it’s slightly left of where Sasha’s standing.

Scene Three:
Description: While in ‘The Dome’ grounds, the party will eventually split into two groups. Fiona will come across a bunch of crates and strange plants either side of a path.
Action: Open the grey loot crate, located to the right of the path.

Scene One:
Description: Fiona will get $1,000. Which is nice.
Action: It’s part of the story, so you won't miss it.

Scene Two:
Description: Some time after the intro credits, Fiona will enter a bustling plaza called the 'Hub'.
Action: When you mouse over the well-dressed Bigshot, you'll get an option to pickpocket him. He’s wandering around near the right of the screen, having a phone conversation.

So much for a spoiler-free guide.

Scene One:
Description: Rhys and Fiona are assembling a team of specialists.
Action: Depending on your choices earlier in the game, you may have the option to contact Felix. If you do, said character will guide Fiona to a stash of money to help out.

Someone has already made a very detailed guide on how to get each character for your team. Check it out for further details.