How did Johnson survive the explosion?

Oddly enough, that's one of the few things in the movie that is actually true to the real life story. The mounties did string a few sticks of dynamite together, after first warming them so as they would work in the cold conditions (I believe they thawed them in their coats rather than by a fire though), and then proceeded to blow up Johnson's cabin. Albert Johnson survived the explosion because he had taken refuge is a small foxhole that he had dug into the floor, which had protected him from the explosion and the collapse of what was left of the cabin. So as far as the film goes, I just assume that Bronson did the same.

It is kinda funny that one of the parts of the story that the film is actually true to appears to be one that most people have the hardest time believing...

As Adec said. Also... dynamite explodes at an angle upwards. If you're in prone position, you should survive the blast easily, even if you're relatively close to the sticks.