First, download the live iso of your choice (I used VL 6.0 Light Live).
Next, you will need to extract the contents of the iso to your usb stick. For this step you could use some kind of software to extract the iso or you could use mc or you could mount the iso.
For the mc method, make sure your usb stick is plugged in and mounted and then open a terminal and type "mc" (no quotes). Then navigate to your live iso. Enter the iso. Once inside, you can copy all the stuff in the top directory of the iso onto your usb stick which is probably somewhere in /media. Maybe in /media/disk.
To mount the iso without mc, open a terminal and type:
mount -o loop /path/to/iso/name-of-iso.iso /mnt/loop
That should mount your iso into the /mnt/loop folder. You can then navigate there with your file manager and copy the files to your usb stick.
Once you have the files copied to the usb stick, look on the usb stick in the extracted directory named boot. Somewhere in there will be a script called liloinst.sh. Open a terminal there and run that script with ./liloinst.sh
This will install the lilo bootloader on your usb stick and make it bootable. It will also set up a "slaxchanges" folder to save changes that you make will running from the usb stick (such as moving, copying, changing files...). You may get some error messages but it *should* still work fine anyway.
Safely remove your usb stick and plug it into another computer. When the computer starts booting, either check the bios to make sure the computer is set to boot from usb first or (if it's available) call up a one-time boot menu (F12 for this for Dell computers). Once you do either of the previous things and it starts booting, it will boot all the way up to the desktop and there you go.