The manual states:
Boot to the LiveCD, logging in as demo, and click on the MEPIS Install icon once you are looking at the desktop. When prompted for a password, enter root.
"Logging in as demo" means to enter demo
as the user and the password of demo
(as stated elsewhere in the manual) and then hit enter or the blue arrow.
Give it a few seconds, THEN you should be at the desktop, where you'll see the install icon.
The manual for the next version of MEPIS is under review, and I think it could be written a little clearer, so I'll make that suggestion.
About the dual boot, I'm no expert, so check out the MEPIS wiki
or MEPISlovers forums for some basic info and free free to ask for help.