The best course of action for anyone really is to heed the warning ...
It amazes me, given that 'Miranda Rights' form a common link in TV shows,etc., just how many American arrestees, if you believe 'reality' shows, break down and 'fess up! AND how many non-Americans think they have 'Constitutional rights'.
Then we have the UK model: Open your mouth now and we'll check out your story/harass your witnesses OR we'll discount your alibi if you get one later.
Then we have the Canadian Bill of Rights/Constitution which really let's you shut up; to refuse to even give your name; to even refuse to respond to police. Of this I have personal experience. Canadian police cannot fingerprint, DNA sample or photograph you unless you are charged and DNA only after a judge convicts you.
I never respond to police in Canada IF I know I have committed no infraction. After my last 'don't talk' session, in which the cops made many mistakes, a couple of years pass and I receive a nice cheque for $17, 861. Damages and legal fees.
This would not/could not happen in either the USA or the UK.
The moral: Know your rights, exercise your rights. I know my rights in Canada and they include the right not to speak to police. And I know how they can work for you.
Saying nothing and demanding a lawyer, are words every one should know. Most other legal points in the article are jurisdiction dependant.
One other thing is common between these three Common Law countries - they ALL use the Reid Interrogation System. (reid.com) The cops are experts at interrogation, most of us are not although saying "Ah, the Reid System" during the early part of an interview throws most cops. It means they can't follow their routine. Study the Reid web site and understand cop strategies.
Re-read the article where it says: One of the main aims of the initial interview is to shut down any potential “Get out of jail card”, such as claiming that evidence was planted or “I let my neighbour use my PC as his was broken”. It is also used to identify evidence that could potentially be used to mount any defence.
Just ask for a lawyer and say absolutely nothing. BUT REMEMBER THIS IS VERY HARD.