You might want to search for some threads on this since there are always a lot of people asking the same question. Anyways, the Nexus is very easy to root. Search for tutorials and ask questions in the rooting forum. Some phones have very easy one click rooting methods but I'm not sure if the Nexus does yet. You might want to at least unlock the bootloader as soon as you can because that performs a factory reset, but there isn't really any way to break the phone doing that and it's very easy to re-lock the bootloader if you need to for warranty issues.
As for advantages, rooting allows you a lot more customization mostly. Look up a tour of Cyanogenmod or something to see what features are common in a lot of ROMs. I've installed a blue softkey mod with menu and search buttons plus a battery percentage indicator as well as a ROM with a lot of new features. You can install custom radios to improve your signal strength and custom kernels to control the CPU clock speed and voltage. That might sound complicated but they're easy to install and usually drastically improve battery life.
Do some searching on rooting and if you have specific questions ask them in the root forum. I think it's very worth rooting, just make sure you know what you're doing going into it and your phone should be fine.