If you just want a lesson in using hashtags (#) go HERE.
The home page of Tweetchat.com has simple 1, 2, 3 instructions on how to use it HERE.
For the first North & South Tweetchat, we used #RichardArmitageNS.
If you follow a hashtag on Tweetchat.com, it will automatically update your feed every time someone posts using the hashtag in their tweet. If you participate from http://tweetchat.com/, your tweets will have your chosen hashtag automatically added to the end, so you don't have to remember to do it yourself.
Armitage Watches include:
Check the calendar tab (above) for dates and episode information.
Another way to follow is to use the search option on Twitter like this one HERE. In my experience, this does not refresh as quickly as Tweetchat, so you may see more of a lag in comments. And you will have to remember to add the # tag to the end of your tweets, or people following on Tweetchat may not see your comments until they check their regular Twitter feeds later.
I'm sorry I don't know much about Tweetdeck or Hootsuite, but I imagine if you use those clients you know enough about Twitter that you do not need any lessons from me.
Any other questions, feel free to contact me and I will try to help. @ArmitageWatch (or @StacieMakeDo if I don't answer the other quickly enough for you ;)