There are a number of ways to use Multics today.
One option is to run it locally under an emulator. The source code that's available should run (under emulation) on most Linux systems, Mac OS X, and Windows, even the RasPi. See the Multicians site for details (a cookbook is available).
Another option is to telnet (or ssh) to a public access system. I don't know of any ones running on original hardware1 (IIRC a few years back there were two on the 'net, one in Texas and one in Germany). One current system that I know of (running emulated on a Xeon server) is at
ssh email@example.com or
telnet m.trnsz.com Login using
login Guest To log out use
logout For more info see the website
The Living Computer Museum in Seattle also has a Multics system but (apart from the front panel) it is entirely emulated.
1 The last Multics site on original, physical hardware went offline in 2000.