You can order online and over the phone @PraxxtorCruel. If you have a car in mind, email your nearest Motability dealer to check the lead time as some vehicles do take considerably amount of weeks from order to delivery.
Your chosen dealer would request your PIP entitlement letter as well as your ID to submit the application to Motability.
Also have a look at the Motability deals and offers topic as some do offer reduced AP.