Whether you should sue after a car accident depends on how severe the car accident was and how bad the damage to the vehicle was in the car accident.
If the car accident was just a minor fender bender and no one got hurt and there wasn't much damage to the vehicle then suing for the car accident really would not be worth the time in court and the court costs.
In that case you should just exchange information and contact your insurance company about the fender bender and then get estimates to repair your vehicle.
The other drivers insurance should pay for the damages done to your vehicle.
If the car accident was more severe and your car suffered major damage as a result of someone else's negligence or it was a company vehicle and you got severely injured or someone in the vehicle died or got severely injured as a result of that car accident then suing the other driver or company for the accident would probably be a good idea.
You'll need to hire a good car accident lawyer who knows their way around the courts in the car accidents to help you win the lawsuit.
The lawyer will help you prepare for the day in court and will do the needed paperwork to get you the settlement after the lawsuit is won.
You can then get your settlement in one lump sum or use a service such as JG Went Worth to get your payments in one lump sum faster or have the settle paid out to you monthly.