Well.. stainless steel pretty much welds just like regular steel (in so much as its a pretty simple welding procedure)
Galvanised steel, (which is regular steel coated in a Zinc like covering) is the monster when you are welding.
so, the answer is, that really its pretty easy to weld the two, you could use regular metal filler rods to weld the two, and it would bond pretty well.
the problem comes when you think about your application (why are you welding the components) -- both stainless and galvanised are rust proof/resistant when they are not damaged (by welding) -- when you weld galvanised metal, you need to prepare the weld area by grinding off the zinc surface and exposing the raw metal, only then can you weld... -- now that area is not protected by the zinc and will rust --so if you wanted a rust free application, you have messed up the surface at the area of the join.
Stainless steel, can be welded with a stainless steel rod/filler, which will not rust, however.. when it gets too hot, or blends at the weld surface to the regular metal, it too will start to rust at the weld site (very slightly).
You also mention welding machine... well, this also depends on thickness of material and frequency of task, you can use MIG, TIG, and ARC welding to do this task... and they will be proper welds (the mig and tig would handle thinner material welds) and they will be proper welds.. As mentioned, the only thing that is not proper, its that the site will now rust.
NOTE: the response is a DIY level response, if you are performing engineering grade welds for high stress scenarios.. you would not really use these two materials together in the first place... But when you have the metal or the need.. one makes a plan.