Okay, so basically the whole thing is made up of 'subreddits', which are all completely separate and have their own submissions (either text or links) and pages. The idea is that over time you build up a collection of subreddits that are relevant to your interests by subscribing to the ones you like and unsubscribing from the default ones that you don't. Your front page is like the 'top picks' from all your subreddits at that time, and the all button next to it is like that but with all subreddits, not just the ones you're subscribed to.
You can make submissions to different subs by using the links on the right, although some subs may have certain rules you should follow so it's always a good idea to read what's in the side bar. Sometimes new users find their posts don't appear in the 'new' section of that subreddit (all submissions ordered by most recent first), in which case you need to message the mods to get the spam filter to recognise you.
Submissions and comments are ordered based on upvotes and downvotes, which are supposed to help bring the most valuable content to the top and get rid of all the rubbish/spam, but there are mixed results. Typically you should upvote things you like, leave alone things you don't and downvote things that are insulting/trolling/against the rules, although a lot of people seem to downvote things that they don't like even though it goes against
reddiquette. You can view your own sumbissions and comments by clicking your username in the top right, and when you get replies the envelope will turn red and you can click on that to view them.
Other than that it's pretty simple, there are formatting help dialogues to help you when making comments and submissions.