How do you effectively submit an opponent in UFC Undisputed 2010?

Solution 1:

The best way we found to guarantee a submission was to weaken your opponent beforehand. With enough kicks to the ribs from standing, your opponent will get rocked very easily. From there, you can do a takedown, slap on a submission, and probably submit him because his stamina is just that low. He can still get out if your shine is bad or if your ratings are terrible, but in general, attempting a submission on a fighter who is rocked is almost guaranteed to work.

^ Taken from IGN AU

Here is an eHow i found on the topic that may be useful.