To me, “next Tuesday” means the Tuesday that comes next week.
For example, on Monday, October 11 and Wednesday, October 13, “next Tuesday” means October 19.
Whereas on Monday, October 18, “next Tuesday” means October 26.
“This Tuesday” refers to the Tuesday that comes this week, which on Wednesday would refer to yesterday, and on Monday refers to tomorrow.
Similarly, “Last Tuesday” is the Tuesday that came last week.
Without any descriptors, day names by themselves mean the next such day in the future unless used in the past tense.
“He will do it on Tuesday” means the next time there is a Tuesday, which on Monday would mean “tomorrow” but on Wednesday would mean the following Tuesday.
In the past tense, day names mean the last such day which occurred.
“He did it on Tuesday” means the most recent day that was a Tuesday.
Not everyone may agree with this analysis, but in my experience this is what most people mean when they use “this”, “last”, and “next” with day names.
english.stackexchange.com/users/39/nohat
This clearly has no definitive answer - usage varies between speakers.
To me, "next Tuesday" means (strictly) the next instance of a Tuesday, although I just wouldn't use it on Sunday or Monday (preferring the day after tomorrow/tomorrow or an unqualified "Tuesday", which generally refers to the current week, past or present).
However, I accept that this is personal and that others may sometimes mean "the next Tuesday but one", bizarre as that may seem.
This assumes that I know what day it is, which cannot always be relied on.
english.stackexchange.com/users/1625/Albert Herring
My preferred use is to specify "this coming Tuesday" or "the Tuesday after next" when I talk about days, specifically because of the ambiguity of what "next Tuesday" could be.
That's just my preference, though.
english.stackexchange.com/users/1552/munin
My answer to another question making a similar inquiry about using the phrase "next week"—
The issue isn't as definitive as you might think.
Ultimately, it comes down to what interpretation of "next" you consider to be correct.
For example, the American Heritage Dictionary (4th ed) defines 'next' simply as Immediately following, as in time, order, or sequence Following this definition, "next weekend" will always mean the weekend with the start date in closes proximity in time.
If the phrase is used during a weekend, of course, you'd be referring to the weekend following the one you are currently experiencing.
However, the issue gets more complicated if you look to other definitions.
The Oxford American Dictionary has a specific definition for 'next' when used in the context of time: (of a day of the week)
nearest (or the nearest but one)
after the present : not this Wednesday, next Wednesday Here, we're given the choice
: it can either mean the weekend with the closest start date, or the following one (as specified by the parenthetical addition or the nearest but one ).
This definition has come about mostly because of usage development.
Many words and phrases in the english dictionary have meanings contrary to their technical definitions, and yet are still used commonly and considered valid.
Thus, while technically "next" implies immediate sequence, it is used in other ways (which dictionaries like the OAD have accommodated for validity), so it's really a matter of personal preference.
For example, it is unlikely that I will even use the phrase "next weekend" during the week, because some people might be confused as to what I am referring to.
Instead, I will say "this weekend," unless it is currently the weekend, in which case I will say "next weekend."
english.stackexchange.com/users/9718/Ryan Atallah
"next-Tuesday" would be better said as "Tuesday of next week".
Thus, the answer to your question would be "on Tuesday".
english.stackexchange.com/users/1414/Christopher Bottoms
There are several possibilities: This Tuesday is the Tuesday of the week that we are in.
Next Tuesday is the Tuesday of the week we'll be in after this one.
This appears to be the most common usage, and makes most sense when you're trying to distinguish between imminent Tuesdays.
They both refer to the same date; this (coming) Tuesday, which is the next Tuesday on the calendar from today.
This Tuesday refers to this (coming) Tuesday, or the Tuesday that comes next on the calendar from today.
Next Tuesday refers to the Tuesday after this (coming)
Tuesday, or the Second Tuesday on the Calendar from today.
This usage seems rare... but is actually what I understood for many years (although I was aware that people didn't always share my views).
Some people switch meanings on Tuesday.
For example, they mean (1) on Sunday and Monday, but (2) from Wednesday onwards.
Occasionally, I've heard people talking who have different understanding of the terms, but who happen to come to the same conclusion about the date of an appointment!
And then there's "Last Tuesday"...
but let's not get started on that one!
All in all, unless you know that you speak the same "calendar language" as someone else (and it isn't always obvious) your best bet is to: Use a different way to express yourself, "Tuesday of Next Week", for example.
Use dates, "Tuesday 11th".
Or get out your calendar and point.
english.stackexchange.com/users/628/Kramii
I know someone who would confuse it even further with the usage "Tuesday first" meaning the first Tuesday after today - where most people would interpret that as meaning a Tuesday which landed on the 1st of a month.
english.stackexchange.com/users/4335/neil
At what point does  next Tuesday  mean    the next Tuesday that will come to pass     and no longer    the Tuesday  after  the Tuesday that will come to pass?   And, when does the meaning switch back?
Which day does "next Tuesday" refer to?
english.stackexchange.com
<meaning><idioms><time><this-next>
english.stackexchange.com/questions/3841
english.stackexchange.com/users/61/Chris Dwyer
This question has no definitive answer and usage varies between speakers. Many people may claim that "next Tuesday" is the Tuesday of the week after this one. However, some people will use "next Tuesday" to refer to the next instance of a Tuesday. It means the Tuesday that is coming next week. The next time that day occurs, just as in the past tense it means the last time that day occurred. However, usage varies depending on the individual speaker's interpretation, which can depend on how "next" is interpreted. The Oxford Dictionary has a specific interpretation of "next". People may have different interpretations, but still  manage to meet on the right day. There are better alternatives that could be used for clarity such as "the Tuesday of next week". Alternatively, using and pointing at a calendar is suggested to avoid any confusion.
This question has no definitive answer and usage varies between speakers. Many people may claim that "next Tuesday" is the Tuesday of the week after this one. However, some people will use "next Tuesday" to refer to the next instance of a Tuesday. The issue isn't as definitive as you might think. There are several possibilities. Often "This Tuesday" is the Tuesday of the week that we are in and “next Tuesday” means the Tuesday that comes next week. It is often better to specify "this coming Tuesday" or "the Tuesday after next" when I talk about days, specifically because of the ambiguity of what "next Tuesday" could be.   All in all, unless you know that you speak the same "calendar language" as someone else (and it isn't always obvious) your best bet is to:   Use a different way to express yourself, "Tuesday of Next Week", for example.  
This is open to some interpretation.  It often means "the Tuesday in the next week", although it can also refer to "the next instance of a Tuesday". The answer to this question is subjective and will depend on personal preference. Many people may claim that "next Tuesday" is the Tuesday of the week after this week. However, some people will use "next Tuesday" to refer to the next Tuesday after today.
Usage varies depending on speakers' interpretation. It can depend on how you interpret "next" Other definitions can cause confusion to the intpretation of next. There are better ways of saying it. Use dates as an option. Or take out the calendar.
There are several possibilities. Often " This Tuesday" is the Tuesday of the week that we are in and “next Tuesday” means the Tuesday that comes next week.  It is often better to specify "this coming Tuesday" or "the Tuesday after next" when I talk about days, specifically because of the ambiguity of what "next Tuesday" could be.   The issue isn't as definitive as you might think. All in all, unless you know that you speak the same "calendar language" as someone else (and it isn't always obvious) your best bet is to:   Use a different way to express yourself, "Tuesday of Next Week", for example.  
Many people would refer to "next Tuesday" as the Tuesday during the next week after this week. The answer to this question is clearly subjective and depends on personal preference. Some people would use "next Tuesday" to refer to the next Tuesday after today.