You can download a -current iso, burn a dvd (in this case I'd recommend getting a DVD-RW media) and boot from it and install it like any other version.
Secondly, you can download the -current via rsync to a local mount point, boot up and instruct the ncurses installer to get the sources from that mount point.
Thirdly (and it's the way I recommend most) you can do it with slackpkg. How? Chances are that you already have slackpkg installed (if not get it from here: http://www.slackpkg.org/
Install it and edit the /etc/slackpkg/mirrors file and uncomment the line that has the address to the -current server you like the best. Then it's just a matter of simple steps and (depending on your connection and systems specs) some time. The steps are to be run as root and are as follows:
# slackpkg update
# slackpkg install-new
# slackpkg upgrade-all