How to use "no pun intended"?

The vast majority of times, "no pun intended" is used precisely to draw attention to the pun that was just made.

Since the preceding pun may not be readily apparent, it can help the reader go back a few words and catch the pun. Personally I don't use this phrase much, but I'm not a very punny person.

If you're actually afraid that something you wrote can be misinterpreted as a pun, then simply reword it, so that you wouldn't need to use a disclaimer like "no pun intended".

'No pun intended' IS a pun!
Not so much a contradictory answer, however, I do miss another aspect of the phrase "no pun intended". Thanks to Jeff Richards on episode 135 of the Probably science podcast I can now never hear the phrase without hearing:

Nope, unintended!

Thought that side of the phrase had to be told here as well. This does underline Dimitry Brant's answer even more, I feel.

Most of the time, in my opinion, if one goes to the extent of pointing it out by saying 'no pun intended,' it was intended, and the reason they are pointing it out is so the other party 'gets' it, because in many cases, the other party doesn't 'get' it unless one points it out, since it is a double entendre.

In writing, I write, 'pun intended.' When speaking, I usually don't say 'pun intended,' I just pause for a moment and look bemused at the other party to wait until they get it, and if they don't, I finally ask, 'get it?'