Android: Today, CyanogenMod, the newly formed corporation behind the popular custom ROM of the same name, released an Android app that will guide you through the process of installing the ROM to your phone. You'll need a Windows PC to complete the process, but it's as simplified as you can get for installing a custom ROM. You don't even need root!
However, you will need to have a device on the supported list, which at the moment consists exclusively of Nexus devices, an assortment of Samsung phones and some HTC One variants. You can download the app from the Play Store below, but make sure you're at a Windows machine with a USB cable before you begin. And don't forget to back up your data!