Take the form and your money into the passport office with your passport if you are in Bangkok you will need to make a appointment to go they will look over your form and take your money and give you a receipt for your money and form
You have to wait and once your passport has arrived they will inform you
You take your old passport with you and they will cut a corner of your old passport and then return it to you with your new passport and they will give you an form for the immigration office to fill in and you will need one more for the thai immigration to fill so you will have two forms for the thai immigration
You need two copies of your passport one for the old and the new passport
Now if you are on a retirement visa they will ask you for your bank book and a full years statement from your bank, this is what happened to me even though its not on the website for the passport renewal, I have to go to Bangkok immigration