Simple Apex class to return a list of strings

You can't instantiate a List like that using an integer. You don't need to explicitly specify how much items are going into the list when it is created. Instead, just remove the integer:

//Instantiate the list
String[] myArray = new List<String>();

You're logic in your loop seems to be incorrect as well. Specifically, myArray's size will always be 0 when you instantiate it. Change your loop logic to:

for(Integer i=0;i<length;i++) {
   // code
}

You want to generate a List of strings based on the i variable. You will want to change your internal logic to:

//Populate the array
myArray.add('Test ' + i);

// Write value to the debug log
System.debug(myArray[i]);

Finally, you want to return that Array. You need to change your method so the return type is no longer void by changing its signature:

public static String[] generateStringArray(Integer length)

then it is just a matter of returning that array at the end of your method:

return myArray;

This would bring it all together as:

public class StringArrayTest {
    //Public Method
    public static String[] generateStringArray(Integer length) {
        //Instantiate the list
        String[] myArray = new List<String>();

        //Iterate throught the list
        for(Integer i=0;i<length;i++) {
            //Populate the array
            myArray.add('Test ' + i);

            // Write value to the debug log
            System.debug(myArray[i]);
        } //end loop

        return myArray;
    }//end method       
}// end class

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Some more info on Arrays and Lists, Loops, and Class methods for future reference.

Problem is on the following line

String[] myArray = new List<String>(length);

Lists in Apex do not have constructor for creating lists of predefined length (see doc). This should solve the problem:

String[] myArray = new List<String>();

P.S. to satisfy your requirements, you will also have to change for-loop condition like this:

for(Integer i=0;i<length;i++) {

Here's my shot at it:

public class StringArrayTest {

    //Public Method
    public static List<String> generateStringArray(Integer length) {

        //Instantiate the list
        List<String> myArray = new List<String>();

        //Iterate throught the list
        for(Integer i=0;i<length;i++) {

            //Populate the array
            myArray.add('Test ' + i);

            // Write value to the debug log
            System.debug(myArray[i]);

        } //end loop

        return myArray;

    }//end method       
 }// end class