If you go to My Chat Profile at the top right of the page, that will bring up your profile. Under your profile picture in the left column Find Latest Posts will take you to a list of your latest posts. Below that Find Latest Threads takes you to the latest threads you have started.
Under the Christian Chat.com banner, click Chat Rooms and Forums, this will bring up a list of of the Forums, with a teaser of the latest post made therein. Click, say, Bible Discussion Forums, and that takes you to a list of the threads. Clicking the name of a thread takes you to that first post of that thread, if there are numbers then clicking a number takes you to that page in the thread. At the center top of the data page clicking View First Unread will take you to the first new post since you last visited the thread.
Once you visit a thread, you are subscribed to it. Go back to Chat Rooms and Forums under the banner at the top, under that choose Quick Links, then Subscribed threads. That will bring up a list of threads you have visited. Headlines in bold mean there are new posts.
Back under the Chat Rooms and Forums, clicking New Posts will list all posts as they are made.
That should get you started. You'll pick up more as you explore.