Assuming you have installed Ubuntu using a usb drive and hence you are familiar with creating bootable USB drive. If not refer to this.
Step 1. Write the ISO of the distro you want to install to a USB drive
Step 2. During installation most distro will automatically detect the existing Ubuntu installation. Consequently they will give option to install the new distro 'side-by-side' to Ubuntu or you do it manually. Select the option you are most comfortable with.
Step 3. Complete installation, reboot.
Step 4. On boot up, a screen will come up that will have installed operating systems as a list and you can choose. Mostly it waits for 10seconds for a user input, otherwise boots into a default distro.
Step 5. You can edit the Grub file to change the boot time behavior (wait time, default distro etc)
Hope this helps,