Assuming you mean the human-based soldiers when you refer to "Combine soldiers" (properly known as "Overwatch soldiers") - they are originally fully human, who are then modified with bio-tech and mechanical augmentation and "programmed".
It seems that there is an induction process - firstly, humans are recruited into the Civil Protection forces. These guys have little in the way of augmentation (allowing rebels to infiltrate the forces easily enough).
Although it's not made clear in the games, there do seem to be incentives for agreeing to the augmentations required to make you an Overwatch soldier - privileges that are also taken away as punishment for bad performance. You get to see some of the processing facility where augmentation is undertaken at Nova Prospekt in the game - it would appear that this is also not always voluntary.
There's also a "stripped" model of an Overwatch soldier hidden in the game libraries - it shows some of the modification done: