The sickening crunch and out of control motion of two cars meeting the wrong way can be very scary. But after the accident is finished, you're actually just starting a long process of accident assessment and potentially repairs. However as you start the journey from roadside shock to the hands of someone with auto technician training, certain steps can make the process more smoothly.
On site:
The first thing to look for is your safety. It's okay to move your vehicle over to the shoulder or out of harm's way, as long as you don't leave the scene. A first priority is dealing with any injuries or danger. If it was an accident of any magnitude and if anyone was hurt, even minimally, call emergency services, either 911 or the local police telephone line. Your local jurisdiction will also determine the extent of the damages necessary to notify the police.
At this point you need to exchange information with the driver of the other car. It can be very stressful, especially since both of you may be worried that your insurance rates will increase, that you need to prove fault and that the other person will be angry. Leave who is at fault to the police and the insurance companies, after things have been looked over in a detailed assessment by qualified technicians and an auto body estimator.
Make sure you get the make and model of the other car, and if you have a camera, thankfully found on most mobile phones, take pictures. Consult with the police as necessary, and send your car off to the garage. You may need to call a tow truck. One other productive thing you can do is make a sketch of the accident scene while your memory is fresh. If you have to give testimony in court, confidence in your memories will work to your advantage though.
At the Garage:
Generally though, once your vehicles are in the hands of the mechanic it's a matter for the insurance companies to negotiate with each other. Your car will need to be assessed, both to get an accurate picture of the sort of damage that occurred and if your car is road worthy or repairable. Auto mechanic programs teach their graduates just these sorts of skills, which can provide forensic testimony if the other party in the accident disputes your claim, for example if you claim to have been in a particular location in an intersection and the other party claims that you weren't, the impacts on both cars will show both the point of contact and how fast you were going. The mechanic will also help your insurance company decide if you get a cash payout and can go car shopping if your car is totalled, or how you will rebuild and get back on the road.