It really depends upon several factors, including where your suit is filed (civil, state or federal court), the congestion of the court's calendar there, as well as the complexity of your case, who your defendant is, and other factors. Suffice it to say getting a case to trial could take years. Here's a general description of the process if your case is in NY State Court.
Once your case is filed, a process delineated by the Civil Practice Law and Rules ensues.
First, the Summons and Complaint must be served upon your adversary.
Then there is a period of time in which your adversary must serve an Answer to the Complaint upon you (or your attorney) that can be up to 60 days or more depending upon the court and who your adversary is.
After the Answer is filed, the discovery process begins. A request for judicial intervention (RJI) is filed, generally by the plaintiff, seeking a Preliminary Conference. This conference is where the schedule for Discovery is determined.
The RJI also triggers a court case management process that is designed to keep cases moving toward trial or other resolution. When this begins, the court sets a "Standards and Goals" date that is theoretically the date by which your case must be resolved either by trial, dismissal, settlement or some other ending. The courts try hard to stay within the standards and goals dates, so you can use that date as a rule of thumb for when it will be resolved.
Once your RJI is filed, you can check the e-courts website to track your case. If your case is in NY State court, just google ecourts or go to www.nycourts.gov/ecourts/index.shtml and follow the steps to find your case.