Since I was a kid, I’ve always been a bit confused:
Is “Next Friday” synonymous with “This Friday” or does it mean “The Friday after this one”?
–SSgtBaloo
There is no general agreement on this – so I generally say either “this coming Friday” or “Friday of next week,” depending on which one I mean – and if the person I’m talking to says “next Friday” I will ask for clarification.
That’s a usage question, not a grammar one. For most people in my experience, “next Friday” means the next ensuing Friday, whether it be Wednesday and meaning the day after tomorrow, or Saturday and meaning the Friday in next week.
I believe standard British usage distinguishes between “next Friday” and “Friday next” – on today, Wednesday 10/27/04, the first would mean Friday 10/29, and the latter, Friday 11/5 – Friday in next week.
I agree with it being the one that comes next.
There’s a common phrase in parts of the south - “Friday a week” meaning the Friday after the next one that occurs-could be from 6 to 13 days away. .
It’s definitely a usage question, and one my husband and I argue about frequently. Okay, today is Wednesday. If I’m talking about the Friday that happens in two days, I’ll say “this Friday”, but if I’m talking about the Friday that’s still nine days away, I’ll say “next Friday”. To hubby, “next Friday” means the next occurring Friday, whether it’s one day away, or six. You’d think after more than 20 years together, we’d learn to speak one anothers’ language. 
This is how I do it. But because of the ambiguity I usually end up clarifying anyway.
The replies so far mostly match my own thoughts. “This Friday” pretty invariably means the upcoming Friday, but “next Friday”… it depends on who’s saying it, who’s hearing it, whether it happens to be Friday, and - if so - whether everyone involved happens to remember that it is.
It’s probably best to avoid that phrase and smack it with a baseball bat if it comes too close.