Generally speaking a visa is something you buy before you travel, that allows you to enter a country for specific reason. On entry, your passport is stamped with a date that you have to leave by, depending on the visa you bought. An extension is something you buy inside Thailand at an Immigration office - it's a stamp that permits you to stay for a specific period of time and for a specific reason (e.g. Retirement/Marriage to a Thai/Work).
If you have a Thai bank account, they can print out a statement with the address in English. If you're working, they will accept a letter from your employer confirming your address. Otherwise a Thai driving licence or a 90-day report receipt showing your address.
If you're in Thailand you apply through VFS in Bangkok or Chiang Mai. Depending on how busy HMPO are (in Liverpool) it can take anything from 3 to 10 weeks.