To post a "New Topic", simply go to the appropriate Forum, and flick the New Topic switch at the top of the Forum list, or under the "Forum Options" dropdown - note that you must be Logged In to preform this operation. When the "Post Box" pops out, fill'er up!
If you wish to Reply to an existing thread, you'll find a "Quick Reply Box" at the bottom of each individual thread - you can also use the Full Reply Form linked there, which is quite the same as the form used making a New Post. If the post you want to make is not directly relevent to the thread, it's preferred that you "Post a New Topic", rather than "hijacking" an unrelated one. If you want to "Quote" a particular post in your reply, use the button(s) at the bottom of that post, which will jump you to either the Quick or Full Reply box as you choose - you can carry on typing what you wish to add after that quote, or you can pare the quote down to just the relevent point you wish to respond to. You can also use the plain "Reply" buttons there to jump.
If you want more information about a posting member, click on their user name and you'll see a list of links to PM them or see their public (to members) profile, etc. There is also an "Edit" button that will only work on your own posts, to bring up the "Edit Post" box, so you can change that post of yours that you forgot to Preview, or so you can delete it altogether. Note that you cannot delete a post that is the first in a thread (a "NewTopic" you posted), if there have been replies to it. Only you or a moderator can delete your post or thread, not another member.
Note that when you hit the "Add Reply" there may be some delay before the message shows up, and sometimes the delay can make it seem like nothing has happened - have patience, sometimes there might be a dozen other posts happening at the same time, or the general internet connectivity might be slow. If it turns out that you hit the button twice and actually made 2 posts, open one of them and delete it!! If you didn't Preview the reply before adding it, and see an error or omission, click the Edit icon and make the changes, rather than making a seperate additional post.