Without more context, and with a general understanding of how video games are set up here is my understanding:
Get is being used here to mean achieve or accomplish.
with your player would refer to the fact that "You" are in fact not actually participating in the football game, but rather "You" are controlling a "Player." Therefore "Player" is sort of a device that you are using to achieve the "assists."
As in the Wikipedia article you linked assist is a countable noun that is "given" or "awarded" by the scorekeepers (or other?). Some usual verb that describes the receiving of a countable noun because of an accomplishment are "recieve" (obviouly), "get" or "earn."
Therefore the phrase is saying the game will ask **You/Your-Player to perform an assist three times." The following sentence is likely what will happen after you accomplish this task - unlock a trophy, new mode, proceed to the next training stage, etc.
Hope this helps!