In steaming the milk you are setting out to "volumize" it by adding tiny air bubbles to the milk, what are called "microbubbles". (Another expression you'll hear that means the same thing is "stretching" the milk). Place the tip of the steamer of your espresso machine just a little below the surface of the milk. Your aim is to suck air into the milk by forming a whirlpool near the top of the milk. Do not have the tip of the steamer above the milk or so close to the surface of the milk that the steam is blowing air into the milk: you are wanting the air to be sucked into the milk.
Do not move the pitcher up and down in an action that takes the steamer head in and out of the milk. Unfortunately, this is something that you'll see happening at quite a few coffee shops, and when you see it you can be sure the "barista" is poorly trained and you are about to be served an inferior drink.
Tilt the pitcher slightly so that the air being sucked into the milk is hitting the side of the pitcher near the bottom and is making the milk rotate so that the heat is being distributed and all of the milk is being brought into contact with the steam as it circulates around the pitcher.
By the time the milk has come to the correct temperature for your drink, it should be volumized to the extent that it has approximately doubled in volume. As I said before, make sure you leave sufficient room for this expansion to occur when you start out otherwise you will have to stop the steaming process before it is at the right temperature.
The milk should have been volumized by the addition of tiny "micro-bubbles" of air. It shouldn't be full of large bubbles which is what will happen if you lift the steam tip above the surface of the milk and blow into the milk. If however there are a few larger bubbles on the top of the milk when you are done, you can remove them by banging the pitcher on your countertop to break them
That's the basic preparation of your milk. However if you are going to be making a "flat white" or macchiato you have one more step to follow. That is to fold the micro-bubbles from the top into the milk at the bottom using a spoon or by swirling the milk in the pitcher until it becomes one consistent velvety and rich mixture. Use this milk for the preparation of flat whites and macchiato coffee. But here's what I do to save all the messy clean up when steaming your espresso milk: I use an Aerolatte whisk. Using the steamer in your home espresso machine can be a bit of a hassle. For a start, you need to have a machine that has a separate boiler for the water used to steam the milk. The reason for this is that to make steam, the water has to be heated a lot hotter than the water that is used to brew your espresso. If your machine has only one boiler for both brewing the espresso and steaming the milk, then don't use the machines steamer. (I give you an alternative below.) Some machines I found also cause the pressure in the espresso side to increase to the point that you get "blow back" when you remove the filter cup from the machine and coffee grounds will be blown all over your kitchen. (This was a fault of the "Briel" espresso machine I owned for a while; other than that fault, it was a good machine though. When using the steamer you also need to be meticulous in keeping the steam head clean of milk so that the the tiny hole that the steam comes through doesn't become blocked with dried milk, not to mention obvious health and hygiene reasons that demand you keep the steam head clean, milk being such a wonderful breeding medium for bacteria
For all these "drawbacks", until I bought my current machine which has a double-boiler with separate steamer boiler, I personally dispensed with using the steamer at home, and used a wonderful little gadget called an "Aerolatte", which is basically a battery-powered whisk. I used a mug in which to heat the milk in the microwave oven; 1 minute is the perfect time for bringing the milk to the right temperature in my case. You then use the Aerolatte to achieve the same volumization effect talked about above. Again, position the whisk head sufficiently below the surface of the milk for it to cause a vortex that sucks air down into the milk. I works perfectly, and all it takes to keep the whisk clean is to run it briefly under some running water after each time you use it
You can buy an Aerolatte at Amazon.com. You can get them in several finishes. The one I have at home is the matt black. I recommend getting the stand that goes with it too so you can keep it conveniently next to your espresso machine.