User defined String array size/input Java

Your code has a number of issues with it that I tried to correct as per below:

import java.util.Scanner;
import java.util.*;

public class SportsLeague { 

  public static void main(String[] args) {

    System.out.println("Howdy sports fan!");

    String menuSelect;
    Scanner keyboard = new Scanner(System.in);
    List<String> teamsArray = new ArrayList<String>();

    do {
      System.out.println("Please pick an option from the list below:");
      System.out.println("1) Create League");
      System.out.println("2) List all teams");
      System.out.println("3) Record a win");          
      System.out.println("4) Record a loss");         
      System.out.println("5) Quit");          

      menuSelect = keyboard.nextLine();

      //since you're making a menu, switches are better
      //this is especially so since your program exceeds 4 options
      //which is a generic rule of thumb for readability
      switch(menuSelect) {
        case "1":
          System.out.println("How many teams should I make?");

          //reset the teamsArray, so that you can create a new league
          //you may want to change this if you want
          teamsArray.clear();

          //get the number of teams with which to create names for
          //by converting the line from the keyboard to an integer
          int teams = Integer.parseInt(keyboard.nextLine());

          //now iterate over it and assign values to the array by
          //prompting the user for the info and saving it using
          //the add() method
          for ( int i = 0; i < teams; ++i )
          {
            System.out.println("Team " + (i+1) + "'s name?");
            teamsArray.add(keyboard.nextLine());    
          }
          break;//break is required here

        //print out the contents of the teamsArray
        case "2":
          for ( int i = 0; i < teamsArray.size(); ++i )
          {
            //print out the elements within the arraylist using the "get()" method
            System.out.println(teamsArray.get(i));   
          }
          break;

         //implement for the other options...
      }
    } while(!menuSelect.equals("5"));
  }
}

One: You had your class named "main" - which is borderline okay, but should be capitalized. However, I took the liberty of renaming it to something more pertinent to your problem.

Two: You should use ArrayLists instead of "normal" arrays where possible - as you reallocate, deallocate memory and other options much better than you would do with a regular array.

Three: You should use switch - since your number of cases exceeds 4 (which is a general rule of thumb when writing menu code for readability).

Those aside, I think this should suit your problem quite nicely.

In your case, the loop was being read twice since you did a keyboard.nextInt(). Although, you read the integer correctly, the newline character had not been read. Therefore, when keyboard.nextLine() was called, it read the newline character - which gave you the impression that you had looped "twice" and had not picked up your second output (when in fact it had, but you did not know, or see). This is also why when you had it as a string, it captured the newline character and the captures worked flawlessly.

UPDATE:

Edited to use static arrays versus ArrayLists:

import java.util.Scanner;
import java.util.*;

public class SportsFan3 { 

  public static void main(String[] args) {

    System.out.println("Howdy sports fan!");

    String menuSelect;
    Scanner keyboard = new Scanner(System.in);

    String[] teamsArray = new String[0];

    do {
      System.out.println("Please pick an option from the list below:");
      System.out.println("1) Create League");
      System.out.println("2) List all teams");
      System.out.println("3) Record a win");          
      System.out.println("4) Record a loss");         
      System.out.println("5) Quit");          

      menuSelect = keyboard.nextLine();

      switch(menuSelect) {
        case "1":

          //set the number of teams within array to 0

          //check to see that the number of teams that the user has enetered does not exceed the maximumTeamsize

          int numteams = 0;

          System.out.println("How many teams should I make?");   
          numteams = Integer.parseInt(keyboard.nextLine());

          teamsArray = new String[numteams];

          for ( int i = 0; i < teamsArray.length; ++i )
          {
            System.out.println("Team " + (i+1) + "'s name?");
            teamsArray[i] = keyboard.nextLine(); 
          }
          break;

        case "2":
          for ( int i = 0; i < teamsArray.length; ++i )
          {
            System.out.println(teamsArray[i]);   
          }
          break;

         //implement for the other options...
      }
    } while(!menuSelect.equals("5"));
  }
}