userText = userText.toLowerCase(); // userText is declared earlier in the program
                                       // as the user's input. Setting this to lowercase
                                       // so it doesn't say "a" and "A" are two different
                                       // characters.
    int uniqueChars = 0;
    for (int i = 0; i < lengthText-1; i++) { // lengthText is declared earlier
                                              // as userText.length();
        if (userText.charAt(i) != userText.charAt(i+1))
            uniqueChars++;
    }
    System.out.println("there are " + (uniqueChars + 1) + " unique characters in your string.");
}

public static int countUniqueCharacters(String s) {
    String lowerCase = s.toLowerCase();
    char characters[] = lowerCase.toCharArray();
    int countOfUniqueChars = s.length();
    for (int i = 0; i < characters.length; i++) {
        if (i != lowerCase.indexOf(characters[i])) {
            countOfUniqueChars--;
        }
    }
    return countOfUniqueChars;
}

char[] letters = new char[26];
    for (char c : letters)
    {
        letters[c]=0;
    }

v  = sort(v);//your sort method

int count = 0;
for (int i = 0;i< lengthText-1; i++)
{ if v[i] == v[i + 1]  {
        i++;
    } else {
        count++;
    }
}

list = new ArrayList<String>();
for ( /*   */ ) {  // same for loop you wrote
      String character = (String) text.charAt(i);

       if(!list.contains(character)) {  // note the '!'
            list.add(character);
       }
}

// and finally
int quantity = list.size();

public static int countUniqueCharacters(String input)
{
    String unique = input.replaceAll("(.)(?=.*?\1)", "");
    return unique.length();
}

public static int countUniqueCharacters(String input)
{
    String unique = input.replaceAll("(?i)(.)(?=.*?\1)", "");
    return unique.length();
}