Java Pig Latin Translator
I would suggest the following points to make this programme more object-oriented:

Try using a collection object provided by Java instead of using array

String[] word = userInput.split(" ");


could be

List&lt;String&gt; words = Arrays.asList(userInput.split(" "));


or using external library Guava

List&lt;String&gt; words = Splitter.on(" ").splitToList(userInput);


Avoid comments where you can.

In this case I can see you can easily avoid comment if you can wrap up the particular code snippet with the meaningful name. For instance You could take the user input and breaking it in a list in separate class and call the class from your main

List&lt;String&gt; words = new UserInputHandler().getInputAsList();


Try to use foreach loop over for loop:

You can easily use the foreach loop to iterate over words

for (String word : words) {
    String pigLatinWord = translateWord(word); // Translates each word individually
    output += pigLatinWord + " "; // Joins the translated word back into the output
}


Again as suggested before you can wrap the code inside for loop in a separate class so that you could call

for (String word : words) {
    output = new PigLatinTranslator(word, output).translate();
}