If your vehicle is repairable, and you either have collision coverage or the at-fault party has taken responsibility you can take your vehicle to the shop of your choice.  The insurance company that will foot the bill is going to want to inspect and photograph your vehicle and do a repair estimate, which will then be the basis upon which the body shop will be paid. You probably want to meet the body shop manager, discuss how you want the repairs done and monitor the repairs. 

Give the at-fault party or their insurance carrier an opportunity to inspect and photograph your damaged vehicle before you modify or repair it.  Failure to do so opens the door to some arguments you don't need.

You may want a rental vehicle during any period your vehicle is disabled or being repaired.  Sometimes, but not always, the insurance company of the at-fault party will arrange a rental for you.  This is called a "direct-bill".  You may be required to pay a cash deposit or have it charged to a credit card even if a direct bill is authorized.  In some cases, you will need to rent a vehicle and then seek re-imbursement.  

In any case, you will want prompt repair of your vehicle to get it back promptly and also to avoid the insurance company terminating the direct bill before the vehicle has been returned to you or having the insurance company deny part of your claim for re-imbursement.  Keep an eye on minimizing rental charges to avoid having the insurance company not fully reimbursing you.

If your vehicle has substantial damage and or the vehicle is older and not of high value, the insurance company may say your vehicle is a "total loss."  They will then use a company [which they maintain is neutral] which will value your vehicle as it was pre-accident.  Such valuations especially when from the at-fault company tend to be low.  Your may be better off using your own collision coverage and letting your carrier obtain the re-imbursement from the other carrier.  But don't confuse obtaining re-imbursement with representation. Insurance companies represent only their own interests - only a lawyer can represent you.