"All combat happens vainly, no matter how artful it is, if the steps for it are not executed correctly" - Joachim Meyer
There are three steps in Meyer:
The basic "step" is outlined in detail in the Dussack cutting drills rather than the chapter on stepping in the Longsword.
Basically to go forward you move your lead foot forward a pace. Job done.
After that there seem to be several options:
1. you can recover this lead foot, like a mini-lunge
2. or take another step forward on the lead foot (particularly in the Rapier) to a proper lunge distance
3. or gather your rear foot to take another step forward
"pull your rear foot up to the forward right one, so that you have another full step forward with your right foot to go"
To cut and step backwards, usually to retreat and maintain measure, you move your rear foot backwards with the action (e.g. with your cut or parry) and then pull your front foot back towards your rear foot, thus moving away from your opponent.
"as soon as this hits, step back with your left roof [the rear foot in this instance] and cut with the long edge from below at his left arm"
The Single step
"Secondly, there are also steps to the sides which are described by the triangle, namely thus: stand in a straight line with your right foot before your opponent and step with your left behind your right towards his left, and this is the single"
This is the common side to side step that everyone in HEMA knows and can do. The below step makes it clear that the translation/Meyer is slightly wonky, that it should start with "step with your right foot toward his left." Some people confuse this step with the step forward. I've added emphasis to the quote above which makes it clear that this is not primarily a step forwards. A step forward wouldn't make a triangle, which is a defining feature worth commenting on.
You will note with the above you will have made two triangles: hence double step.
Cutting without moving
All German systems say you should support your cuts with steps and Meyer is no exception. However, this does not necessarily include instances when stepping would be pointless such as with some parries and in the handiwork, i.e. if you are already in measure and don't need to gain or loose distance to your opponent then stepping would only slow you down from an action that should be very, very quick.
Interesting note, as pointed out by my friend Martin Cribbin, people do not see much improvement in their cutting speed by practising the action of their arms. This is because what actually slows people down is that they cannot move their feet fast enough. So to cut faster people should be practising to move their feet faster. If you look at the plates in Meyer the guys are often travelling so fast that their feet are flying off the ground.