Tailors primarily make armor and related items. The armor tailors can make is of type cloth, which is of most use to casters (mages, warlocks and priests).

Making money from tailoring is not a reason to choose tailoring. It isn't really a money maker at all. Until you reach the point where you can get recipes that very few can make you won't really see any income, and those recipes take either a lot of effort or a lot of luck to get (or a big load of gold). Even then a lot of those recipes require  Primal Nethers to make, which means for each sell you have to get your hands on a  Primal Nether first (only reliable way to get these is through heroic instances).

One way to make money from tailoring is making either  Primal Mooncloth,  Shadowcloth or  Spellcloth. You can make all three kinds as they're on different cooldowns (each are on a 4 day cooldown though), but you can also specialise and then get twice the amount of the type of cloth you have specialised in. This means the profit margin goes up greatly when crafting those. If you have tailoring this high then chances are that you'd want to craft either the Frozen Shadoweave, Primal Mooncloth or Spellfire set for you own character (for more information about these sets see the Bind on Pickup Tailoring Items section).

All of the specialisation specific sets require 26 of their type of cloths, so you can imagine that with a 4 day cooldown timer it'll take quite some time before you can even start to think about making the cloths for profit. When you do reach that stage though, you'll be looking at a very nice low-maintenance income.

Bearing the above in mind, I suggest tailoring mostly to people that would really like the awesome bind on pickup epic armor sets at endgame for their character.

Tailoring is different from quite a few of the other trades, in that it doesn't particularly benefit from having a gathering skill or another trade. Most of the ingredients needed are drops you get from killing humanoids and the threads you will need are bought from vendors.

Because of the above reason quite a few guides recommend pairing Tailoring up with Enchanting as Enchanting doesn't rely on other trades either. This can be a good choice as it is nice to be able to disenchant green items you make in tailoring that you can't sell at a reasonable price.

Personally, I'd say that this combination is ok - but very very slow for making money whilst levelling. I cannot stress enough the benifit you would gain from levelling up with two gathering trades instead. I know it's fun to make your own gear as you level - but it's also fun to be able to buy your epic mount when you reach 60 ^.~

When you reach endgame and decide tailoring is the craft for you (it has some excellent epic bind on pickup items - did I mention that?) I'd suggest keeping one of your gathering trades instead of taking up two crafting trades. If you have another high level character that can do the gathering to ensure income, then I'd recommend, as most other guides do, that you pick up Enchanting to go with Tailoring. In The Burning Crusade especially you can really see Enchanting and Tailoring being paired up more. For the last 35-30ish levels you'll need tons of  Bolt of Imbued Netherweave, that all need 2x  Arcane Dust to create. This means that you'll end up spending lots of gold on getting these last skills as a tailor if you aren't an enchanter yourself (or have a nice friend that will disenchant lots of greens for you).

If Enchanting isn't your thing then the two next ones to choose from, in my opinion, are Alchemy and Jewelcrafting. These two will need gathered ingredients though, which you'll need to either farm on an alt or buy at the auction house. But they are both very useful trades for casters.