You would file an adversary proceeding with the bankruptcy court alleging some violation of the bankruptcy code
oftentimes in conjunction with some other type of violation. The most common type of bankruptcy lawsuit is for non-dischargeability of debt due to some type of fraud or misrepresentation.
If you are a debtor there is no filing fee to initiate a lawsuit; however, there is a strong likelihood that the judge will refer you to state court to hear the matter because of a recent case Stern v. Marshall.
If you are a creditor then you will need to pay a filing fee. You need to allege that the person has broken the law with a document called a complaint. The complaint needs to be filed with the applicable bankruptcy court and served on the person whom you are suing. You will need to consult with both the Federal Rules of Bankruptcy and the Local Rules of your district in order to determine the exact process in your area. If you are seeking to have a debt you are owed determined to be non-dischargeable, then you will need to make sure that your case is filed by the deadline to object to dischargeability. This is usually about 60 days from the First Meeting of Creditors
The service requirements are less strenuous in bankruptcy court, so you can serve a lawsuit via US Mail (of course you would want to serve it certified, return receipt). Many districts have forms that you can use.
Once the lawsuit is filed, then you can start the discovery process. Mediation is always encouraged after a case is filed to reduce the strain on the court system. This may be a great way to settle out your claim.
There was a recent supreme court case Stern v. Marshall, that has caused a lot uncertainty on which cases can be heard in bankruptcy court and which ones cannot. In the past the bankruptcy courts authority to make final judgments was very broad. Now; however, there is greater limitations on bankruptcy judges. I hope this helpful. Please let me know if I can clarify for you further.