To access Solo Challenges go to Ultimate Team from the main menu and then select Solo Challenges on the far left.
Currently the easiest to complete is the Introduction category in the Getting Started tab. Currently it consists of two challenges against very easy AI that barely throws strikes. One challenge requires you to throw 10 punches and the other requires you to throw ten kicks. Once you've done the requirement finish the match and move onto the next.
Each challenge will reward you twice, once for meeting the minimum requirement to start the fight, and then again for completing the actual challenge. If you cannot get a challenge to start it's probably because you don't meet the minimum requirement which can be seen on the challenge requirements screen. The only minimum requirement in this category is to have 5 bronze items which is very easy to obtain.