As long as you got the insurance information from the other party, contact his insurance company. Don't forget to contact your insurance company too. An adjuster should be assigned to handle your case (either from your insurance company or his insurance company, depending on who you call). Keep your contact with this person, who should have already received a copy of the police report. If he/she doesn't have a copy of the traffic collision report, provide him/her with one (you can get one from whichever agency prepared the report, which is assuming that you notified the police).
The adjuster will want to get a statement from you (probably recorded) so give truthful answers to the adjuster (because this could be used at a later time in court). The adjuster should eventually send you a letter advising you whether the insurance company has accepted the claim.
The adjuster will probably also advise you to bring your car to a garage of their choice - a preferred vendor, but you don't have to do this - or if you have something in writing from the garage you went to - so that your car can be evaluated (if it's a total loss, based upon the damage to your car and its value).
If your claim is accepted, the adjuster will have a check sent to you to cover the loss. The adjuster will also send you a waiver / release, which should ONLY say that you are releasing the company and its insured (the person who hit you) from claims for any damages to your car (you'll need to sign this before you can get the check). Be sure it doesn't say anything about waiving any claims you may have for bodily injury (unless you'e negotiated a settlement for that too).
That's all the information I have. Hope it was helpful.