For professionals that are expected to actually do 8 hours of work a day, expect to pay anywhere between $50/hour at the bottom end (typically, offshore contractors,) and $250/hour+ for lead programmers in major US cities for contract work, or from a high-quality agency like Laetro. (I’ve used Laetro for art, don’t know if they also do programming.)
Hobbyists have a different schedule and expectation. If your budget is extremely limited (certainly if it’s less than $10k,) that’s probably the best approach. Find some forums where you can find like-minded people, where your good-looking concept art and description of what’s unique about your game can find someone interested in helping out, and offer minimum wage plus a cut of the profits or something.
Expect any project to have a day to a week of setup just to get to know what the game is, where the code lives, and so on, and then between a day and a month per “feature,” because “features” can vary largely in size.
To get a good estimate of what your game will actually take, you need to share a much more detailed plan than “a simple card game.” You don’t need to share the exact art, but you need to know what screens are available, what the user does on each screen, and whether there are special game rules, game effects, animations, and so on, that need to be integrated. You also need to be clear on where the art is coming from, and what format it will be in. Just bringing a piece of art into a game can be anything from five minutes to several days, depending on the quality of the source.
Typically you will hire someone with a background you can verify. You do this by looking at previous work, and by looking at historical profiles on places like LinkedIn or MobyGames or whatever, and you’ll also ask for personal references you can verify. You’ll typically pay a small retainer up front, and you’ll then get some amount of progress to see and make milestone payments. Exactly how this works out, depends on the specifics of the contract, and the contractor. Also, you can frequently negotiate a reduction in rate, for a bigger chunk up front.
In general, the whole point of a contract developer, from the developers point of view, is that they rent their time, and take much less risk on the quality and success of the actual game. To do that, the developer needs to charge a fair amount of money, to compensate for anything from “health insurance” to “time not working while looking for the next job.” Therefore, contract developers are generally more expensive than hiring someone outright, and a lot more expensive than partnering up with someone in a fifty-fifty setup.
