Method 2 (Standard): Download the XexMenu 1.4 installer, copy it to a USB using Horizon or USB Xtaf GUI , then run the installer via your existing homebrew launcher.
Method 1 (For beginners): Burn the default.xex and Media folder to a CD/DVD as a "data disc." Insert it into the 360. The console will auto-launch XexMenu.
Let us know in the comments what homebrew apps you keep on your HDD alongside XexMenu! Disclaimer: This post is for educational purposes. Modding consoles may violate terms of service and local laws. Always own legitimate copies of games you back up.