I'd just write the code in as simple a way as possible.

package com.ggl.testing;

public class MyString {

    public static void main(String[] args) {
        MyString myString = new MyString();
        String string = "abcdefghij";
        String pattern = "defg";
        System.out.println(myString.indexOf(string, pattern));

        pattern = "ghij";
        System.out.println(myString.indexOf(string, pattern));

        pattern = "asdf";
        System.out.println(myString.indexOf(string, pattern));
    }

    public int indexOf(String string, String pattern) {
        int length = string.length() - pattern.length();
        for (int index = 0; index <= length; index++) {
            if (patternMatch(string, index, pattern)) {
                return index;
            }
        }

        return -1;
    }

    private boolean patternMatch(String string, int index, String pattern) {
        int i = index;
        for (int j = 0; j < pattern.length(); j++) {
            if (string.charAt(i) != pattern.charAt(j)) {
                return false;
            }
            i++;
        }

        return true;
    }

}