D.B.Moody is right about secondary vessels falling out of favor. I started brewing when racking your beer to a secondary was standard practice for all beers, so I did it for years. I started skipping it earlier this year and have found my beers to be clearer. I dry hop in most batches, and I haven't had any more issues with sediment than I used to when I used secondary vessels. Obviously YMMV, as different people all seem to have different experiences. I've stuck with leaving beer in the primary fermenter until kegging because it's easier and it means less oxygen in the beer.
You should also note that some people use "secondary fermentation" differently. Typically, it just refers to moving the beer off the yeast to a secondary fermenter to condition. It's a misnomer because there really isn't another fermentation cycle going on; the yeast is just cleaning things up, if anything. But sometimes people use "secondary fermentation" to mean literally another fermentation cycle, like when you add fruit to a beer after active fermentation has ended. The sugar in the fruit will kick up another round of fermentation. Technically, using sugar to carbonate in a bottle does the same thing. That said, it's safe to assume that most people are talking about a second fermenter.
On dry hopping, it's just the process of throwing hops into the beer after active fermentation has finished (and for some beers, during active fermentation, but since you're starting out, only do that if a recipe calls for it specifically). You get more aroma and some flavor from doing this. I really like it! I usually dry hop for about five to seven days because I throw the pellets in and wait for them to drop to the bottom. Some folks prefer to dry hop only for three days or less out of fear of the hops starting to taste grassy or vegetal, though I've never had an issue.
