Depending on the programmer, it might connect to your computer via serial port or parallel port or USB or a combination.
I just picked up a low cost Willem to get re-started with. I haven't programmed a chip yet because I just got an eraser yesterday. But, the programming process should be fairly quick. Of course, it depends on the size of PROM you're programming, but I think I remember it taking about 10-15 minutes when I was doing college projects.
Here's a website that describes a highly efficient programming algorithm that takes 2 minutes instead of 12 to program a 128k chip.
http://www.geocities..._algorithm.html
To put your game binary on a ROM chip, software on your computer works with the burner to transfer the specified file into the chip.
The Willem I got is not the most sophisticated unit around, but others here tell me they've used them effectively. If you want to go high volume or high speed, spend more money.
With luck, someone more experienced will come along and put a finer point on it for you. (By now, you may have already figured it out first hand)