This is the easiest way yet how to jailbreak your iPhone. This method works only if your firmware is 3.13 or older. To find out what is your current firmware see here. iClarified has some excellent tutorials on how to jailbreak or unlock all firmware versions up to 4.10.
First open your iPhone's Safari browser and go to http://jailbreakme.com . JailbreakMe is a userland jailbreak by @comex that is quick and simple. It does not require reinstallation of your iPhone firmware if you are running a supported firmware version and can be performed right on the iPhone via MobileSafari. It is advised to you sync and backup your iPhone first before proceeding. Slide the button to jailbreak.
The website will do all the jailbreaking for you using a PDF exploit that was discovered for version 3.13 and older. Your jailbreak is finished when you see the Cydia icon on your homescreen.
If your iPhone is carrier locked, the next step is to unlock it. Open Cydia, wait for the updates download to finish and tap Manage. Tap Sources and add http://repo666.ultrasn0w.com/ to the repository (if it's not already added). The "0" in "sn0w" is the number 0 not o. Next install Ultrasnow to unlock your iPhone. You should see the message "Your phone is activated".
After that you might want to install Installous to be able to download and install cracked & free iPhone apps. Go to Manage > Sources and add the Hackulous repository: http://cydia.hackulo.us . After that search for Installous and install the app.
You should see the green Installous icon on your homescreen. From here on you can browse and download any apps for free. Please be reminded though that you may lose all those downloaded apps if you sync your iPhone with iTunes. To overcome this you might want to download your ipa files from websites such as Apptracker.org, drag the files to the App section on iTunes and sync them from there. Either way, Installous is needed to overcome the DRM limitation imposed with officially purchased apps.
Again, iClarified has everything you need to know about jailbreaking or unlocking your iPhones and iPod Touches.