Progress. A knocked-out creature tames only when it eats by itself, after its hunger has dropped. Food that is not its preferred kind fills its hunger without moving the taming bar, and when it runs out of food the bar starts to go down. Force-feeding food does not speed taming up: in one player's test it even dropped the progress to 0.
Effectiveness. Taming effectiveness falls whenever the creature eats food left in its inventory, and when it takes damage while unconscious. Torpor is kept up with Narcoberries or Narcotics; these are force-fed with the use key, and Narcotics raise torpor by 40 points over 16 seconds. If the creature wakes up, every item in its inventory is lost. For non-violent tames, progress resets if you take too long to feed again or move too far away.
Levels. For a creature using the ordinary taming bonus, bonus levels are the wild level × effectiveness ÷ 2, rounded down. A Lv.150 wild creature at exactly 100 % would therefore gain 75 levels; slightly lower effectiveness can give 224 instead of 225. This is an example, not a universal cap: species, variants and map rules can use different wild levels. Later experience levels are a separate limit, so check the creature and the current server rules rather than assuming every tame has the same maximum.
05:00. Every day at 05:00 Thai time all wild creatures are wiped so the maps can respawn, and a creature you are still taming is wild, so it is removed too. Warnings start in chat 60 minutes before.