More info on rooting

z4root will root many phones running android 2.1 and below. it is the easiest way to root because no computer is needed. just install the app and run. Just as klatuu mentioned, this will just sit there looking like its doing nothing. just wait and it will reboot when its done rooting. 

get it here:https://forum.xda-developers.com/showthread.php?t=833953

For just about all other phones (with a few exemptions) superoneclick will root your phone. They tell you to download the development kit but you do not have to. Klatuu did not have to either.
All you really need is the "ADB" program, and phone device driver.
On Linux, your golden, it will recognize your phone. On Windows, just search around for your phones driver. You can sometimes get the drivers from the manufacturers website, or from google. you can download the driver pack from google without downloading the SDK. just search around.
There is no need to download 300MB worth of software just to get a small program and driver.

3rd party drivers:
https://developer.android.com/sdk/oem-usb.html
Google driver pack:https://www.fileserve.com/file/5bgRBX5

There are some newer phones that have something called "s lock". these are harder but not impossible.
These have to be rooted kinda like klatuu did it. manually pushing files over, then some terminal kung-fu on the phone. after that, its clockwork mod to the rescue.

all these programs have detailed forums/faq/comments on what devices do and dont work. please read and make sure you are performing the correct procedure for your specific phone.