On an Android phone, there are 2 ways to set up Gmail. The best one (right one IMO) is to use the Gmail app. You can still use the Email app but it doesn't sync the contacts and calendar.

Like Midknyte says, if you set up the correct app (Gmail) the contacts and calendar should sync just like the email.

Here is a video from T-Mobile that goes over the basic (initial) setup.

https://www.youtube.com/watch?v=7M5pCU16XiI