Zenkai means "the power you gain from taking high damage".
To get a zenkai, you must get knocked out or killed. Being killed gives a bigger zenkai. The stronger the person is who gave you the zenkai by knocking you out or killing you, the more power you will gain from the zenkai.
The more often you zenkai the smaller a zenkai you will get. Zenkai needs time to recharge to maximum and each time you zenkai the time to recharge increases.
The power of the person causing you to have the zenkai is the most important factor. To gain any worthwhile power from zenkai the person must be stronger than you.