What are the protocols or procedures that follow a public announcement by a minister of his intention to resign, in the Westminster model?
A minister normally resigns by sending a letter to the Prime Minister, informing her of his intent to resign, and normally giving reasons for the resignation. The announcement may be made by the government, or by the minister. The resignation is normally effective immediately.
The minister remains a member of the House of Commons, or House of Lords, since quitting those bodies is an entirely separate matter. They loose their ministerial salary and other services, such as a government car and driver, and in most cases, their security. Some resigned ministers have continued to have security after they'd left their position: notably some past Northern Ireland Secretaries, who were at risk of assassination, continued to have security for years afterwards. I don't know if this still applies.
That's about it, really. The process is probably less controlled by legislation than in many other countries, because quite a bit of the UK's constitution is based on custom and precedent.
A minister is doubtless free to brief his successor if he wishes, but this is not required, and the civil service will brief the new minister anyway.