I have only one bucket. It's a plastic fermenter, rather than a bucket, not that that really matters.
You don't *need* to have a second one, but if you rack from the first bucket to the second one you can get clearer beer. Most ppl recommend going from a fermenter to a glass carboy though. I go straight from my fermenter to bottles/pressure keg.
So in short you don't *need* a second one, but you may want a second one. It will also allow you to have 2 batches brewing at the same time.
Based on what I have read, it seems that the secondary fermenter is considered an intermediate level and optional prodedure. You'll notice a lot of stores that sell glass carboy's for secondary fermentation in their 'intermediate' kit. I have bought all my equipment, but I havn't brewed my first batch yet, but when I do brew my first one in a few weeks, I plan to use a secondary fermenter. I think a lot of "beginners" start out using secondary fermenters as well, it is really a simple prodedure, its as simple as just racking to another fermenter, and waiting, thats it, just have to be careful and make sure you sanitize everything and try to avoid oxidizing the beer.
You can definately brew beer with a single fermenter though, I think the standard time in a single fermenter is 2 weeks then bottle. After one or two batches you might decide you want to go with a secondary fermentation. To upgrade your kit all you will need to buy is a glass carboy, a drilled stopper, and if you want a secondary airlock. The extra airlock would be optional since you could just transfer the airlock from the primary when you move to the carboy, but I suggest buying another one. It is always good to have an extra plus they are less than a dollar.
Either way I think you will be pleased with the results. Let us know how things come out.
better beer can be brewed with a two stage process
$20 for a second carboy
$10 for an auto siphon
$1.50 for an airlock
$.75 for a drilled bung
i think it's worth the investment. now you may want to wait and save that up over the course of your first couple of brews.....but i would encourage buying a secondary.
i even secondary porters and stouts even though i know that they won't clarify much. it allows them to age better since the wort in a secondary is not sitting on a huge trub and yeast cake. and produces much smoother beer over all.