The basic steps as I understand them are:
- Talk to a lawyer
- Sue the party violating the license
- Prove it in court
- Collect damages
Why talk to a lawyer? The lawyer can review your license agreement and the contract and can determine if what the other party is doing is a violation and assess whether the evidence you have is strong enough to prove your case. The lawyer might even be able to advise you as to the wisdom of getting damages awarded vs. simply sending a cease and desist letter as this determination might depend on whether the defendant can actually pay a judgment.
Once you believe that the license and contract will stand up to scrutiny, there is a real violation going on, you have enough evidence to prove your case and the violator has funds to pay damages sufficient to merit a lawsuit, you sue them in civil court. Ask for whatever damages to which you feel you're entitled; statutory damages or more if you can justify it. It helps if you discuss damages for license violations in the contract or the license, but it's not strictly required if you can show damages some other way.
At this point, the party violating the license knows you're serious and will either ignore the lawsuit (and get a default judgement entered against themselves), settle with you out of court (likely for less than the amount of damages you're asking for, as a sort of compromise), or go to court and try to get out of it. If you and your lawyer did your jobs in steps 1 and 2, you stand a good chance of winning in court. It's not a sure thing since you may get an unsympathetic judge/jury or the party violating your license might have an ace up its sleeve.
You've won the case and were awarded the damages you asked for. At this point, most parties are just going to pay (assuming they are able to, see steps 1 and 2) and stop the violation. There's a possibility that they end up not being able to pay, or not being willing to pay, in which case collecting might be a headache, but you should probably cross that bridge only if you come to it.