How do I root the Android emulator? I need root to install an .apk file on the emulator.
The Android emulator gives you root access, you don't need to root it. Check out the emulator page on android.com for details on how to do things as root.
As other mention, you can use the tools from SDK.
But when your not fond of command lines, you can also explore the emulator with the Eclipse ADT plugin.
The plugin integrates a couple of development tools like ADB, DDMS, logcat, etc...
I find it very interesting to connect my phone with usb (enable usb debuggin) and watch how everything works... ;-) But the same can be done for the emulator...