VirtualBox will let you install either 32- or 64-bit version of Ubuntu. Make sure you download the correct version from the Ubuntu site.
When you create your virtual machine, you'll configure it just like building a real pc. When you do this, you'll add at least one virtual hard disk, and one virtual cd/dvd drive. To install Ubuntu, add the Ubuntu iso to the cd drive, and set the system boot order to boot from the cd drive first. When you start the vm, it will boot from the iso, and you can follow the installation prompts.
After you install, it will force a restart. When the VM is just starting (it will show the VBox logo), close the window to shut down the machine. Then edit the VM settings and remove the iso from the cd drive, otherwise it will reboot the live cd.
Once you're booted to the hard drive, you'll want to run updates, reboot, and then install the VBox guest additions from the vm menu bar.