Love the see the interest,
The basics of TTT is D, T, and inno,
Detective, Traitor, and Innocent.
The most simple job you will get off the bat is T, or traitor. If you are a T, kill everyone you can find. But, be careful not to kill your T buddies, they have a big red T over their head. So, just take a second or two not to kill those, otherwise, kill away. The way to know you are T is in the right-hand corner you will have a red T.
The next job is inno. Inno's job to observe. As an Inno you CAN call a KOS, however you must gain proof. Proof can be a taser (you will need to build up credits in order to buy a taser) and then tase a person. It will show up in chat what their role is. Another way is if you see someone kill someone. Note, give them the chance to ID the body, because they might be killing a T. (e on the body to ID it). If the player walks past the body that they just killed, then they are KOS, and you can call it, and kill them. Also, If they ID it, and it's an inno, or detective, then you can kill them, because they just killed an inno for no reason, which means they are either a T or an RDMer. As an inno you can camp as a long as you would like, you're an innocent civilian who is just caught in the wrong spot, waiting to be saved or killed.
The last role is detective. It's like an inno, but you will spawn with a taser, like the one I mentioned before. You will KOS like an innocent, however, the main difference is that you can't camp in one spot, you must be going around the map, trying to ID Bodies, and get credits, to get tasers, and find out who the T is.
Finally, you will need to know some base rules.
No KOSing off of sound or location.
If you hear someone do something and they have things that fit the requirements to make the same sounds, however you did not see them do anything, you can not kill them.
Don't KOS off of skin or hats, or masks.
You don't know if someone has the same skin or hat as someone that may have shot at you, therefore you don't kos off of that.
Please do not RDM.
The most important rule. RDM is what makes the server bad, if you didn't see someone do something and catch their name in the process, (this doesn't go for tasers), you can not KOS them. If someone else calls a KOS, you can follow it, and if the KOS was false, and not on a T, just ask an admin for your karma back through admin chat.
That's the basics of TTT, you can check out this guide on the forums that goes more in depth:
https://www.edge-gamers.com/forums/showthread.php?315978-How-to-play-TTT&p=2981594#post2981594
Of course, you can always go ahead and find one of us on steam, in game, or on Teamspeak if you want someone to help you through the process. (To answer your questions, TS is not required, just where all the admins hang out).
-WaSe