Hello all
I want to sell a second hand car in Torrevieja and need advice. I know that I can hire a solicitor and pay a bunch of money but need to do it myself and save that bunch! Have you done this before so please don't hesitate to tell me the procedure. Thanks a lot.

Depends on your level of Spanish. This is one of the most popular sites.
Coches de segunda mano y de ocasión | Coches.net

I know where to advertise. That's not a problem but where do I need to register the car, which office, how much it costs, etc.

Pay a gestoria, it does not cost that much, if the papers are not done properly you will remain liable for the vehicle, or sell it to a dealer who will complete the process.

You need to go to Trafico ( DGT )

Cambio de titularidad (para realizar este trámite es necesario acudir a tráfico)

Documentación:

DNI o documento acreditativo para extranjeros (Tarjeta de residencia y pasaporte más NIE). Fotocopia y original.

Documentación completa del vehículo: ITV y Permiso de circulación.

Último recibo del Impuesto Municipal de Vehículos de tracción mecánica. En caso de estar eximido: justificante de exención.

Contrato de compra-venta.