You can approach this a number of ways, here are a few different methods:
1. Contract for a specific length of time for a fixed amount, like "we're hiring you for 20 hours a week for 6 weeks." and they get paid on a timeline kind of like a salaried paycheck.
2. Instead of paying for a fixed time frame, Contract based on the artist's hourly fee for a specific number of hours, but have the actual weekly hours potentially vary. So this would be, like "we're hiring you for 20 hours between now and x date" but the number of hours per week could vary. Maybe you do 5 hours this week and 10 hours next week. In this case, the artist would be sending invoices at an agreed schedule for how much you pay them, like a time sheet. Doing a method like this would work well for an artist who needs flexibility, but who you really, REALLY trust to get their stuff done in the allotted time.
3. Instead of doing it based on time, define segments of work based on their worth, and then the artist gets paid when the work is complete. So, like, you would agree on something like "doing this sprite sheet and all the animations is worth x dollars." and when they complete the task they get the x dollars, regardless of if it took them an hour or a week. This can be useful if your project is at a stage where you have very defined segments of work to be contracted out, but it can be more complicated to figure out up front than something like an hourly fee.
Those are just a couple of ways I know about, there are probably other methods that other people can suggest.