I'm learning how to play, and was trying my hand at the intro riff to Smoke On the Water (http://www.youtube.com/watch?v=EorPLmKS-Y0). I can get it right, but the sustain is poor...so the notes become mute or almost mute by the time I am ready to move my fingers up the neck.

I have an Ibanez RGR421EXFM and a Marshall MG10CD Amplifier.

Any ideas on how to get a better sustain...somewhat like the one in this video tutorial?

I'd say it's probably your amp. Those amps are crap anyways.
Bands to see before I die:
Iron Maiden
Foo Fighters
Reel Big Fish
Streetlight Manifesto

Epi LP Standard
Washburn Strat
Line 6 Spider (Yes, I know it's bad)

Ibanez RG3570Z
Digitech Whammy