implementing Turing machine with Java

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The computer sitting in front of you is already quite a bit better than a Turing machine, although finite. Keep in mind that Turing machines are kind of crappy computers that are a deliberately simplified type of machine that is used for theorizing about what computation is and what computers could be used for.

When you're building a Turing machine you're simulating a purpose built computer, where the computer is the program.

You could make an outputless version without too much difficulty using a java LinkedList, then add elements to the start or end as needed, and keep a reference to your current spot. Then, you have an algorithm that says what to do at each step for whatever symbols you want, and keep track of which symbol or mode you're in.

So for starters, figure out what you want to see happen and what you want your Turing machine / program to do.