My preference is to use manwithaplan’s “Friday” and “Friday week”. My family has always used those, and if you are familiar with the “xxxday week” thing, it’s crystal clear (is it used at all in the US?).
Unfortunately, it does seem to confuse some people no end, so I often have to use the “this Friday / next Friday” thing. Definitely my second preference, though.
Next Friday means the friday of next week.
Oh, I mean:
I love cazzle too. 
English is the reason we have so many lawers.
BTW I vote goes to the cazzle camp too. sorry
Well, because usage varies so much, I tend to say something like “You mean this coming Sunday, or a week from this Sunday?”
But I’m distressingly literal-minded sometimes.
People group the days into units called WEEKS.
If you say NEXT (day) you are implying NEXT WEEK on a certain day.
If it was Friday and you said ‘next Friday’ then it would be the very next Friday.
In other words if the day in question is more than six days away you say next. If is is less than six days away no modifying word is used.
hey cazzle waves you popular girl you !
to add my 2c worth, i agree with cazzle!
hey…caz…can ya tell my presence here means i’m really bored g
As someone who makes his living via appointments, I use this technique when scheduling or rescheduling. I don’t always have a calendar handy to refer to “the fourteenth,” but I always use the “this coming Friday” or “Friday of next week.”
Incidentally, cazzle is correct, and is also loved.
That is all.
I almost never say “next” unless it’s perfectly clear from context what I mean (e.g. it’s Friday, and I say next Tuesday).
If it’s Monday, I say “this coming Friday” and if I mean the Friday of next week, I say “Friday of next week” or “a week from this Friday”, and usually quote the date as well.
I’m coming to this quite a bit late, but:
Far as I can tell, this is not used anywhere in the US. I certainly never heard it before, and in fact erroneously thought it was a typo the first time it appeared in the thread.
And for once I’ll throw my vote with the majority, and go with the cazzle system. No modifier, or “this,” is within the next six days. “Next” as a modifier means seven days away or better, and so on.
I have a similar problem with AC and heat. When I ask someone to turn the AC down, I mean I’m too cold. I’m thinking in terms of turning the machine down, causing it to run less. Invariably, someone sets it to colder.