When writing a formal letter or email, you would start with "Dear Mr Jones," (don't forget the comma after the name if you are writing to a business contact in the UK. Whereas I personally find colon seems to be preferred in the US). 

I realize that physical letters are getting rarer by the day, but still feel it's important to know what to write and how to go about it, should the situation arise when you might need it. 

In a physical letter you would skip a couple of lines down and write "Re:" and fill in the subject of this letter. Or just one line down and tab once to the right. 

I'd suggest underlining the subject line. 

Skip another couple of lines down and start the main body of your letter. Like this:

Dear Mrs Smith, 

Re: Invitation to Grand National at Aintree Racecourse 

Thank you very much for your letter dated 3 February. 

I am pleased to say... 

When writing an email, the polite thing would be to start with "Dear Mrs Smythe," but no subject line is needed as this will be stated in the email header. 

Whether writing a business letter or email, it is important to finish the correspondence with a nice touch. 

More formal examples: Sincerely yours, Yours sincerely, Yours faithfully or even just Sincerely

Less formal examples: Sincerely, Kind/Best/Warm regards, Regards - or in some cases - Best wishes

Informal examples: See you, Thanks, TTFN or just writing your name

Take a moment to think before you hit the send button... 

How familiar are you with this business contact? You obviously want to ensure you get the tone just right. 

Have you already gone on to first name basis, in which case you should probably sign off with “Kind regards, Andrew” rather than choosing “Sincerely Yours, Mr Andrew Brown”. 

Or if the opposite is true and you haven’t yet come past the Ms or Mr, then please bear this in mind and don't finish your email or letter with “TTFN, Stephen"