// Using out:
string MyFunction(string input, out int count)
// Using Tuple class:
Tuple<string, int> MyFunction(string input)
// Using struct:
MyStruct MyFunction(string input)
There is no "best practice". It is what you are comfortable with and what works best in your situation. As long as you are consistent with this, there is no problem with any of the solutions you've posted.
Out parameters are fast and cheap but require that you pass in a variable, and rely upon mutation. It is almost impossible to correctly use an out parameter with LINQ.
Tuples create collection pressure1 and are un-self-documenting. "Item1" is not very descriptive.
Custom structs can be slow to copy if they are large, but are self-documenting and are efficient if they are small. However it is also a pain to define a whole bunch of custom structs for trivial uses.
I would be inclined to the custom struct solution all other things being equal. Even better though is to make a function that only returns one value. Why are you returning two values in the first place?
Note that tuples in C# 7, which shipped six years after this answer was written, are value types and hence less likely to create collection pressure.
1 Every time you allocate a small object off the heap, that puts "pressure" on the garbage collector. The more pressure, the more frequent collections. In some applications is it important to control the amount of collection pressure produced, so allocating a few million tuples unnecessarily can be a bad thing in those applications. Of course, like all questions of performance, don't blindly make changes until you understand the magnitude of the problem.
I think the answer depends on the semantics of what the function is doing, and the relationship between the two values.
For example, the TryParse methods take a out parameter to accept the parsed value, and return a bool to indicate whether or not the parse succeeded. The two values don't really belong together, so, semantically, it makes more sense, and the intent of the code is easier to read, to use the out parameter.
If, however, your function returns X/Y coordinates of some object on the screen, then the two values semantically belong together and it would be better to use a struct.
I'd personally avoid using a tuple for anything that will be visible to external code becuase of the awkward syntax for retrieving the members.
I will go with the approach of using Out parameter because in second approach you would require to create and object of Tuple class and then add value to it, which I think is an costly operation compared to returning the value in out parameter. Though if you want to return multiple values in Tuple Class (which infact can not be accomplished by just returning one out parameter) then I will go for second approach.
You did not mention one more option, which is having a custom class instead of struct. If the data has semantics associated to it which can be operated upon by functions, or the instance size is big enough (> 16 bytes as a rule of thumb), a custom class may be preferred.
Use of "out" is not recommended in public API because of its association to pointers and requiring understanding of how reference types work.