I have been a while in the forum seeing a lot of people talking about trust setting, negative trust, and DT members.
I don't know how you saw and noticed them. You registered this account yesterday only.
How can I know about all of these?
Jawhead gave you link to the guide is written by LoyceV. You should read it if you want to understand the DT system. After which, you can read the topic
Trust flags that is the latest update on the Trust system.
Are DT members have extra power or something?
They are unofficial police staffs on the forum. As DdmrDdmr explained, the trust feedback from DT1 or DT2 members will be displayed by the default DT view (that most of members use as they don't customize their Trust list).
Their trust feedback can be seen and it can be an unofficial power (if you would prefer to worry about their power). In my opinion, the power is not make much sense if you are good member. Only scammers are care more about Trust feedback from DT members. Their scam activities are seriously affected by those feedbacks.
How to be a DT member?
Build up your account, with real contributions and wait for time, luck and recognition from the community -- it takes months or years. Forget about building up your fake trust networks.