If you've been around forums a while, this will probably be old hat. If you're new to forums, however, this will show you how to... well, do the things the title says.
To start a new thread, go to the forum view and click on the "New Thread" button.
That will get you to a screen that looks like this:
Enter a title (and good titling is an art; you want it to catch attention, but also be clear), type your text, and if it's at all complicated (has links, different fonts, etc), it's best to use the preview function first (arrow 1) and then submit it (arrow 2). A few of the other buttons are also identified above.
I'll assume the "Post reply" button is pretty self-explanatory, so I'll move on to quoting. You might want to quote a post if it's not the most recent and you want to make it clear what you're replying to, or you can quote (and edit the quote) to make it clear which sentence(s) of a long post you are replying to. Click on this button to quote:
The result will look like this:
You can do whatever you want [ ]between the brackets[ ] and the result will look like this:
But if you are cutting down and lose a bracket from either end, you'll get a messier post. So when quoting, either quote the whole thing, or make sure {quote=name,number} is all there at the beginning, and {/quote} is all there at the end.