Pig Latin Translator in C++
Couple of issues:

This appends the first letter of the word onto the end.  

       word += word[0];


Since I don't know what "PigLatin" is I can't tell if this is correct. A comment about what is the expected translation is really required so we can understand if this is correct behavior.

This sets the first letter to 0.

       word[0] -= word[0];


Note: NOT the character 0 but the number zero which is an unprintable character (there are no glyphs that represent the number 0). Note the character 0 is represented by the number 48 (in ASCII or UTF-8).

Did you want to remove the first character from the string?

word = word.substr(1); // Gets the substring from 1 to the end.
                       // Assigns it to the variable word.


Adds the string "ay" to the end of word.

       word += "ay";


Sure. Sounds reasonable. But need to understand the expected behavior/

You have a string. Which you are converting into a sequence of words and storing in v.

    std::vector&lt;std::string&gt; v;


But the only thing you do with v is loop over it and get each word to call translate() with. Why not remove the middle man and not use the container at all.

Here You are creaging a loop as long as the string. But each iteration you are taking a word from the string.

    for(int i = 0; i &lt; str.length(); i++){


So this will have a lot of blank words on the end. A better way is to read words from the stream until there are no more words in the stream.

    while (stringStream &gt;&gt; currentWord) {
        // Do stuff with currentWord
    }


Avoid the use of std::endl.

std::cout &lt;&lt; std::endl;


Its probably not doing any harm here. But its a bad habit. The difference between \n and std::endl is that std::endl also flushes the buffer. Manually forcing a buffer flush is usually incorrect. The buffers will auto flush at the optimal time. Program inserted flushing is usually wrong and is a major cause of eniffciency in C++ code.

I would refactor the inner loop like this:

    while (stringStream &gt;&gt; currentWord) {
        std::cout &lt;&lt; translate(std::move(currentWord)) + " ";
    }
    std::cout &lt;&lt; "\n";


Notice the std::move() this moves an object to the function (saves a copy). So at the translate() needs to be changed slightly.

std::string translate(std::string&amp;&amp; word)
{                                ^^  bind a moved parameter.
   // stuff.
   return word;
}