What is the trick to soldering to aluminum bases (like are found on the older Luxeon LEDS?)
The primary problem in soldering or brazing aluminum is cleanliness...oxidation and cross contamination must be prevented. In aviation we use a hydrogen flame instead of acetylene for better heat control. Larger pieces are welded using heli-arc or tig (tungsten inert gas) processes. A skilled operator can "glue" razorblades together.
Soldering to aluminum is indeed tricky. Aluminum oxidizes even worse than copper, so you need a different, stronger flux that you get with most solder. Also, soldering to something like the base of a Luxeon LED means you are trying to solder to a heatsink - so it will be difficult to get the aluminum up to the melting point of solder.
The aluminum bases of LED modules, and other heatsinks, are normally electrically isolated. They are just heat sinks. So before you go to too much trouble, I'd question why you are even attempting to solder to aluminum.
Soldering aluminum is hard but possible. Cover the aluminum surface with mineral oil and scrape the oxide. The oil will prevent it from reforming immediately through contact with oxygen. Then tin the surface with a hot iron and normal leaded solder. Then clean off the oil and solder as usual on your tinned surface.
However as Jon Hirsch said, these bases are not intended to be soldered. You need to apply some heat conducting compound and affix them using screws to the heatsink.
One problem with soldering aluminum that has oxidized is that the melting point of aluminum oxide is (2072 °C) much higher than aluminum itself(660.32 °C) , so by the time you melted the outer coating of aluminum the inside is liquid already. this can be a problem with thin walled parts like tubes etc.