Okay here's how it works (I actually bought the game):
A and B punch left and right, up and down block (also holding up lets you punch high), left and right dodge. Just like Punch Out. You must dodge in the direction where their fist will not be (usually if they move to the right, they will punch to the left, so dodge right. Generally dodge in the direction they go). You must block in high or low for where the punch will go if you decide to block.
ALSO, L and R do special left hook and right uppercut (but you can't be holding up while doing it, so learn to let go of up and press L or R if you are doing face punches). These punches do much more damage but always knock them out of a stun.
The best way to maximize damage is to dodge, then hit them 3 times with normal A/B punches and finish it with an L/R punch. If you hit them 4 times they'll block the L/R punch. A/B punches do 2 damage (unless you hit them when they are just standing there instead of after dodging, then they do 5 damage), L/R punches do 10 damage (a full health bar is 90 damage).
Once past the first fight, you'll start earning cash. You can buy special moves from Da Back Alley, Vic's Gym, and the Arcadium. Vic's teaches you 3 levels of a power uppercut that gives an instant knock down. To do it, hold A+B and press Up. Arcadium teaches 3 levels of a rapid fire punch sequence. Hold A+B and press left or right. Da Back Alley teaches you a nut sack punch (ouch!) by holding A+B and pressing down. All of these require your blue bar to be full.
Da Back Alley can also give you inside information allowing you to hire the ring girl, referree, or mechanic to help you during a fight by pressing Select (once only, then have to re-hire them). The girl puts them in a distracted daze for several seconds where you can punch them all you want (except L/R punches which will bring them out of it). The referree will slow down his count to half speed when you are knocked down if you press select while he's counting, giving you more time to get back up. The mechanic will throw a wrench that damages and knocks down your opponent. Finally the back alley guy can teach you a "Parry" move that's hold down, then press Up+A at the moment when they would normally hit you, and you'll automatically dodge the hit and counter punch. Nice because it works on any punch no matter which way it is coming from.
WHen you are knocked down, rapidly press any and all buttons, including directional buttons, to fill up your health meter and get back up. Every time you get knocked down it will fill up slower. In general if you get knocked down 4 times you won't be able to get enough life in time to get back up. ALSO, when the enemy is down pressing buttons will very slowly fill up your own health meter while they are trying to get back up.
Between regular matches, you will be challenged to special bonus matches. Press L on the map screen to see them. They are things like "beat me without dodging" or "beat me without blocking" or "beat me without getting hit" or "beat me in 20 seconds." If you win the challenge you will get extra cash, lose and you will LOSE cash (you don't lose cash for losing regular fights).
Press R on the map screen shows all your stats and other boxers' stats.
Press Select on the map screen lets you blow money on buying silly hats that the referree will wear during matches...odd..
It's all about reflexes and learning to read the opponent so you can dodge in the correct direction, then punch 3 times and finish with an L/R punch. Repeat until your power bar is full and smash them with a purchased special move. Learn how to avoid their special moves too (some you dodge in a certain direction, some you have to hit them instead at the right time).
Have fun!