Unfair business practices (Business and Professions Code Section 17200 and following) provide for injunctive relief but not damages. It appears from your facts that you have a breach of contract case and perhaps, and difficult to prove, a fraud case for intentional misrepresentation.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
This is a great deal more complicated than is practical to handle as a pro per. You will need an attorney for any realistic possibility of success in this dispute.
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The process for filing a lawsuit under B&PC Section 17200 is the same for any other type of lawsuit. It involves the preparation of a summons and complaint, the filing of the complaint and issuance of the summons, and the payment of the filing fee. The complaint is a document that must be drafted by hand -- it is not simply a form to be filled out.
I strongly suggest you meet with a lawyer to help you with this process, to make sure you indeed have a viable claim under that statute, and to see whatever other claims you may have. There are many fine business litigators on AVVO that can help you.
You will need to prepare and file a summons and complaint for violation of 17200, breach of contract and potentially other theories such as fraud by way of a false promise. I don't recommend representing yourself for claims like that...while you might save a little money up front it will likely cost you dearly as the case progresses. Give me a call if you'd like to schedule a free consultation.