Convert to Upper Case 
System.out.print("Enter A String ~>");
str = scan1.nextLine();  // assume enter lower case
ChangeCh(str);
private static void ChangeCh(String str) {
    // TODO Auto-generated method stub
    System.println(str.toUpperCase());
}
For converting to lower case, its quite similar with the above answer, you just need to modify a bit. I think you can solve it yourself.
Source: Java - String toLowerCase() Method.
To convert Upper Case to Lower Case and Lower Case to Upper Case between a String, use the code below
    public static void main(String args [])throws IOException
   {
    System.out.println("Enter A String ~>");
    Scanner scan1 = new Scanner(System.in);
    String   str = scan1.nextLine();
    String sentence = "";
    for(int i=0;i<str.length();i++)
    {
        if(Character.isUpperCase(str.charAt(i))==true)
        {
            char ch2= (char)(str.charAt(i)+32);
            sentence = sentence + ch2;
        }
        else if(Character.isLowerCase(str.charAt(i))==true)
        {
            char ch2= (char)(str.charAt(i)-32);
            sentence = sentence + ch2;
        }
        else
        sentence= sentence + str.charAt(i);
    }
    System.out.println(sentence);
  }
Note : A (upper case) and a (lower case) have a difference of 32 in ASCII code.