Did you actually run the Mavericks installer??
To amplify the point: You probably downloaded the installer into your Downloads folder.
First: You have a complete system backup, correct? Making one is always (ALWAYS) the first step. Fortunately, Time Machine makes it really easy. It does take some time, though. But, do it.
Then. Open a Finder window. To the left you'll see a column of frequently-needed folders. The "Downloads" folder will be one of these. Double click it.
In this folder you will find the Mavericks installer. IIRC it's a .dmg file-- a disk image. Double-clicking it will effectively mount a new disk drive on your machine. It may or may not pop up an install-me? dialog. If it doesn't, try double clicking the mounted disk image to see if there's an installer (most likely a .pkg file) inside, and then double-click that.
You'll have to say yes to a few questions, maybe type in a password, and then leave the machine alone for a while.
Shortly, you'll have an updated machine. Some things are different in Mavericks, but it's a nice OS, and you get Pages, Keynote and Numbers for free, and they're awesome. (Really, it's rather pathetic how badly Keynote whips PowerPoint.)