This is the way it was done in the old days before mig and tig, but you can weld both quite successfully with some practice.
To weld aluminum you use a small diameter flux-coated aluminum arc rod,and weld just like brazing,bring the metal to melting point and let the rod flow in.
Same for magnesium,except you buy bare magnesium rods from a welding shop and a jar of Flux,warm the welding rod first,then dip it in the flux powder,then melt it in,continuously dipping the rod in the flux.
It is hard to tell when these metals are near melting point,I was taught to gently prod the metal with your rod as you're heating it,when it is starting to get soft add your rod,once it;s flowing it goes great.