There's a fairly simple way to make gold without professions: Sell summons to a pick-pocketable Hagara to rogues looking to get their legendary quest starter daggers, Vengeance and Fear. These are the most accessible rogue weapons, because aside from picking the pocket of the fourth boss in a raid instance, the quest can be easily completed with a 10k gold and a minimum amount of help. These daggers are the best entry-level options for rogues who PvP or PvE, available as soon as they hit 85 and are capable of completing the quest.
If players are raiders, they'll probably get it for free just by being in a raid that gets to Hagara; however, if all they do is PvP or casual PvE through the Raid and Dungeon Finders, they won't be able to get the first leg of the quest finished. Within a few weeks, most rogues who want to start the quest will have started it. Until then, I've heard of non-raiding rogues paying as much as 25k for the opportunity to pick Hagara's pockets.
The first three bosses
To some people, getting a lockout saved to Hagara but not farther will be the hard part. Back when people were trying to get specific lockouts saved in, for example, Ulduar, raid lockouts worked differently. Nowadays, assuming you raid 10- or 25-man normal modes, you can simply swap an alt in for either Warlord Zon'ozz or Yor'sahj the Unsleeping, whichever you do third. This alt can safely swap back to their main and will be forever saved to Hagara, able to extend the raid week after week, even if the rest of the group proceeds to one-shot Deathwing that night.
Once you have a character saved to the first three bosses, the rest is pretty straightforward. You need to clear Hagara's trash to bring the boss out (once a night), and summon buyers to the instance. If they don't have the quest, they can get it from Lord Afrasastrasz. After they pick Hagara's pocket and turn in the next leg of their quest downstairs, the boss needs to be reset to allow the next rogue to do it. This is most easily accomplished by having the rogue throw something and Vanish. Otherwise, once they're kicked from the group, someone can solo-pull the boss; while that person will get killed, the boss will reset. If these methods don't work, apparently waiting 15 minutes always works. Worst case, reform the group and redo the trash.
The trash is not trivial; however, a pair of tanks and healers with some DPS can easily do it in a few minutes. If you use friends for this, give them a cut equivalent to the amount of time they spend. If they spend as much time on this endeavor as you, they should get the same cut. If it's strangers you recruit for trash only, you can get away with paying them a fixed fee agreed upon beforehand. The problem with using strangers is that they will spread the word and possibly compete with you for rogues. Personally, I'd use trusted guildies and split the money evenly.
Everyone is going to be a little leery of this unless they have a sense of security. A pair of ilvl 397 daggers would be a steal at 50k gold on the AH right now, but most people would feel paying 10k gold for a summon seems a little scarier. In order to make the buyers feel more secure, make it clear in your /trade and your /tell what you're promising for the money. If someone expresses any doubts, reassure them that Blizzard would consider anything less than the delivery of exactly what they're paying for a scam.
Assuming the character you're bartering on is a main that looks like they'd have too much to lose by scamming someone for 10k gold, your clients should feel confident that you'll deliver them one Hagara pocket. It'll also help if you can ask one of your early clients to testify in trade that they bought it and you provided the quest.
The other side of the coin is that unless you're careful, it's entirely possible to get taken advantage of by a buyer. If they scam you by getting the quest item and not paying for it, you can probably complain to Blizzard. You're much less likely to get your money, though, since you didn't technically lose anything.
If you invite someone to your group before you receive your fee, you risk the possibility of having them come in and do their business without paying. To protect yourself, don't invite people without receiving payment unless you trust them. Also, if for some reason you do decide to do that, if you've got your wits about you, you can pull the boss as soon as you realize you're being had and kick the offending rogue out of the group while they're a ghost.
Profit per hour
If you have your realm to yourself on a given night, you can probably make way more gold per hour per person doing this than you can with standard "craft and list" businesses. It's not going to last forever, though, because while there will always be new rogues hitting 85, there will not always be a huge number of already-level-capped rogues looking to get their daggers without having to start raiding.
You can get the word out on the realm forums, which can help if you want to have a limited schedule. Unlike set-and-forget businesses with 48-hour auctions, you have to be playing and not doing anything more productive while you do this, which makes dominating a market difficult. If there's competition, try to arrange it so that you offer your services during a time when they don't.
Follow standard best practices for trade advertising: Don't repeat your message too often, or else you'll risk alienating potential clients. Also, include links to the items and the quests, as well as your price. I wouldn't suggest having a price that changes, or else buyers might feel that they can get a better deal by simply waiting.
Maximize your profits with more advice from Gold Capped. Do you have questions about selling, reselling, and building your financial empire on the auction house? Fox and Basil are taking your questions at firstname.lastname@example.org and email@example.com.