Connect your iOS device and click the Jailbreak button. evasi0n will retrieve some information from your device. The device will then reboot and prepare itself for the jailbreak. Don't do anything with your device during this stage.
evasi0n will now install Cydia -- the application that provides access to third-party apps -- on your device. When instructed to by evasi0n, unlock your device by pressing the Home button and swiping the Slide to Unlock switch to the right. You should see a new Jailbreak icon on your Home screen. Tap it and evasi0n will carry on with the final stage of the jailbreak. You can now quit evasi0n by clicking the Exit button.
Your device will reboot, briefly display the evasi0n screen, show the Apple logo, and then show the evasi0n screen again, which details the progress of the jailbreak installation. Finally, your device is ready for you to use in the normal way.
The one difference you'll see is a Cydia icon on the home screen. Tap it and Cydia launches, prepares its file system, and then quits. To then use Cydia as intended, tap its icon once again, choose your user type (User, Hacker, or Developer), tap Done, and the Cydia interface loads.
The version of Cydia you're using may need updating; older versions of Cydia may not support Cydia's newer third-party apps. To do that, tap the Changes icon at the bottom of the screen and then tap Refresh in the top left corner. If any updates are available (as evidenced by green check marks) tap the Update button in the top-right corner of the display. Cydia will download the latest updates and reboot the device.
What you choose to install is entirely up to you. Some people choose to install OpenSSH so that they can remotely access the device's file system via a standard FTP client. However, if you enable this feature, be sure to change your device's root password from the default "alpine," which is used by all iOS devices. Fail to do so and others around you could hack into your device. To learn how to change the password, tap the Root Password How-To link on Cydia's About screen.