Hi, Iforget53. Welcome to the list!
You seem to be asking specifically about donor suitability testing. In my case, I knew when I "matched" my recipient candidates (see below) within just a few days.
But donor matching is just the very beginning of the process. Overall, there is huge variation in how long testing and donor approval takes. It can vary by your Center's work load, your own work and travel schedule, the need to repeat questionable tests, etc.
I was in the process for about 15 months. I wish you a much quicker process. In my case, I actually matched for three potential recipients, each of whom got a kidney (I think from a cadaver) before I was fully approved to donate. The third of these actually went pretty far down the testing road together with me. I ultimately donated to the fourth match.
You have definitely come to the right place to learn about living donation, and to get all types of support from a very special group of people.
To return to the question of time: I suggest you prepare yourself for a long, possibly draining process. As I tell others on this list: think marathon, not sprint.
Good luck!
Snoopy