Reddiver here's a link to the page where you can register for Tearjerkers if you haven't already found it. Many of the folks here on the TD & TTT board are also part of that group. (That's how I found out about them.)
http://www.tearjerkers.net/new_forum/in ... 761b98e685
At the top right there is a clicky for registering. Once you put in your registration you will be on your way shortly.
If you don't get a response back right away, hang tight. There have been some new changes that have been made to that board over the past couple of days so some of the administrators may be a little swamped for the next couple days.
As to dues.. There are none. The only real requirement I've encountered is the need to be able to enjoy the company of a bunch of other like minded camping folks. If you're camping with a group of Tearjerkers be prepared to socialize!

I've camped with a few different chapters at some of their gatherings and I haven't met anyone yet that I wouldn't want to camp with again.
With regard to tee shirts - Once you're on the TJ board, scroll down to the bottom of the main page and you'll see an area where links to products can be found. Alot of chapters have Cafe Press "stores" where chapter specific items can be bought.
Hope this helps.