Google. Plus I've stared at a few books looking them up.
http://www.google.com/#hl=en&source=hp&q=304l+uns&aq=f&aqi=&oq=&fp=8bd4816e1661ba1aI'm a little fuzzy material specs because I've never been taught, just figured this out on my own, but this is the best way I can summarize it.
-AISI-SAE only cares about chemistry (mainly for steel, not sure if it covers aluminum or other alloys systems)
-UNS only cares about chemistry (think like an updated and more complete AISI-SAE system which includes more than steel)
-ASTM cares about mechanical properties, chemistry, and shape/finish/etc. Very complete, but one alloy can show up in many different specs just because it's a different shape.
-Manufacturer specs which usually list things like UNS number and ASTM spec.
-And you've got contract specs, which as I'm sure you know, go are the most important because they tell you what road you follow to the paycheck.
So if you're looking at a MTR, you've got chems and mechanicals. Chems get compared to AISI/UNS/Manufacturer data and mechanicals get compared to ASTM/manufacturer specs.