How much programming (PHP) and logic do you know? If there are no tutorials online specially aimed at creating a support-ticket application then think about what is involved in creating one, then, research and look at tutorials for specific individual things that will help you :)
OK, here goes. Your ticketing system will need a DB, so your first task should be how you're going to store, write and retrieve data. You could go for a relational model (multiple table) or just try to go for a flatfile (single table) solution.
Strange as it seems, a relational model may be easier:
Once you have the DB structure in place, designing front-end forms and displays with back-end DB operations should be straightforward.
You'll need a few 'views' (not to bee confused with the OOP 'view') - depending on whether you're an admin or a member. For the admin:
1) List view (like a forum thread view) listing 'pending' (needs your attention) at the top, followed by awaiting and solved tickets. Ideally there should be a 'sort' function on this to sort the list by datestarted, last response date or status. A filter option too to filter by admin, user or even status. A search facility for key words could also be useful here. If an admin wants to search for previous solutions to copy/paste as opposed to re-inventing the wheel all the time.
2) Ticket view - this page appears when a ticket in the list view is clicked (similar to a forum thread view). It will show all the previous replies for the thread and will have a reply box (form) at the bottom. This will just send data to be written to the DB (an INSERT query). However, the ADMIN replies should be able to be edited, thereby allowing an UPDATE query. A 'change status to solved' button may be useful for the admin, but you may wish to leave this to the member.
For the member:
1) New ticket view: just a form for an INSERT query. The main fields will be: title, ticket text, possibly a help category (e.g. sales, technical etc).
2) List my tickets view: just a list of existing tickets (similar to List view for admin), which once clicked can open the...
3) Reply to ticket view (similar to Ticket View for admin).
ANyway, that's just a bare-bones system. If you're adept with Ajax, you could create just the one page and inject the replies and forms in-place when a thread title is clicked. Hope it helps.
As an additional thing, you could attach an email function so that the member receives an email whenever an admin responds to a ticket.