A lawsuit is an action brought about in a court of law in which one party (the plaintiff) accuses the other party (the defendant) of some kind of legal wrong-doing and wishes to be compensated for it. While filing a lawsuit is a complex activity, withdrawing one as a plaintiff is actually an easy task to accomplish. In many cases, a settlement is reached outside of the court system before the plaintiff withdraws the lawsuit.
Attend the court proceedings and ask the judge to file a "Motion to Dismiss". This is the document needed to end the lawsuit.
File the "Motion to Dismiss". In the motion, you will need to choose if you want to withdraw the lawsuit "with prejudice" or "without prejudice". If the motion is filed "with prejudice", the lawsuit is dismissed and the plaintiff is not allowed to bring the same lawsuit against the same defendant on a later date. If the motion is filed "without prejudice", the only thing that is being dismissed is the current lawsuit, but the plaintiff reserves the right to bring about a new lawsuit against the same defendant at a later date. The kind of motion that is filed usually determined by the out-of-court settlement reached by both parties.
Have both the defendant and the plaintiff sign the motion, date it, have their attorneys sign the motion, date it and turn it into the court. At that point, the lawsuit will be withdrawn and the court proceedings will be complete.