Binoculars; Welcome to Macintosh!
You need to drag out the window from the bottom right corner to fill the full screen. If you haven't already done so, you can hide the Dock using System Preferences>Dock to give you more screen space. Safari will remember this window size setting. If you're still having problems, or resizing windows a lot, you can add a script to your bookmarks bar to do it from
here (it's the one at the bottom).
You can minimize the window to the Dock by clicking the yellow button. Double-clicking on the title bar of the window will also minimize the window to the Dock (if enabled in System Preferences>Appearance).
Don't forget to switch on Tabbed Browsing in the Safari preferences, to take full advantage of the browser.
AppleMacster.