When eating diner out in public or at a friends house?

You should ding a spoon in your champagne glass to get everyone’s attention and then when they are all quiet, stand up, turn around so your butt is facing the table, lift one leg up and let it rip. Don’t forget to take a bow afterwards.

Very simple.  If you can easily avoid something that might offend people, do that.  Just excuse yourself--no one is going to ask way.

If you think you can get out of the room before it escapes, excuse yourself and hurry to the bathroom. If there's a fan, be sure to turn it on first thing.

Politely excuse yourself and go into in the bathroom. If you don't make it to the bathroom in time, politely say, "Pardon me."

i would excuse yourself and go somewhere private

If you're going to write a story, at least make it believable.

Farting is a human function, easily compared to be similar of a bowel movement which often comes with similar sounds and smells.  Thus your fart should be removed to the same environment.  Get to the bathroom. close the door and let it rip.  If it is discovered it is a "shart" instead of a fart, you are also in the right place. 

This is going to come down to your own comfort level of farting in front of other people, and your relationship/connection with the people around you.

That depends - do they have a dog you can blame the smell on?

Just do it right there, and blame it on someone else.