You don't need to go to the Transport office in Nong Soong (Ban Hoy for motorbikes) with the purchaser, (although it might be advisable, as you will need to provide a copy of your passport & therefor trust the buyer with said copy

)...
First step is to go to B2S stationary shop (top floor of the complex, just outside Robinson's), ask for 2 forms:
1/. San Yaa Sur-Kai (25 Baht)
2/. Nang Sur Morb Amnad (25 Baht)
Make sure the cashier rubber stamps these forms with the official emblem, I believe it's called a 'Garuda'.. (half bird/half man emblem)
If you are going to Nong Soong with the purchaser, you won't need the Nang Sur Morb Amnad form.
Fill in the forms together with the purchaser, & they can then do the transfer themself at the Transport office.