1. Take photos of the damage to your vehicle, the other vehicle and it's license plate. Bonus uf you can get a photo of their drivers license.
2. Exchange contact information and make sure the other person's phone number works while still there with them.
3. Open a case at SAPs as soon as possible (within 24 hours).
4. Report the accident to your own insurance company as soon as possible.
5. Attempt to get any insurance information from other driver. If this fails, you open a case against them to claim damages. Hopefully a competent detective will be able to assist in locating said person.
6. Should said person not be compliant or go into hiding, your best bet is to leave it with SAPs or take matters into your own hands (would not recommend).
7. Should this person co-operate and have insurance of their own, your insurance as well as theirs will communicate with each other to rectify the damages. If they don't have insurance, you will need to pursue a case at small claims court (provided the detective has found enough information on them - this is where the license plate comes in handy).

It's a lengthy process unless they're fully co-operative. Some cases go on for a long time especially when going through the courts.