(photo: one of many stovetop espresso units I own, this one is a classic, 4 cup, Bialetti)
1. Unscrew the top portion of the espresso maker from the bottom portion and remove the metal filter/coffee ground holder.
2. Fill the bottom of the unit with fresh, filtered, water (to the top of the bolt on the inside of the base).
3. Fill the metal filter with ground espresso, making sure not to pack the grinds but simply filling the filter with enough ground coffee where a small mound is produced.
4. Insert the metal filter into the base and tightly screw the top unit to the bottom portion of the maker.
5. Place the maker on your stovetop and set on a low burn (it's important not to use a high flame as you don't want to boil the coffee).
6. You'll begin to hear the espresso come up in about 8-12 minutes depending on the size of the Bialetti unit you've purchased. And you'll know that the espresso is done when no more espresso is coming out of the top unit (simply open the hatch and have a look inside). I like to turn off the stove about half way through the brew as the residual heat will finish bringing up the rest of the coffee; if you keep the flame on your pot you run the risk of over boiling / burning your coffee.
7. Stir the espresso in the maker before serving.
A note on espresso beans: like any type of coffee preparation the fresher the bean the better tasting your coffee will be. So, you can buy beans and grind them per use, but it can be a labor intensive and messy affair (espresso beans need to be ground very fine). If you're going to go the "grind every day method", you'll need a high end burr grinder. And remember there is no such thing as an espresso bean, just regular coffee beans that are dark roasted and ground very fine.
My preference is to buy pre-ground espresso from Illy or Kimbo. After all, espresso is meant to be a "quick" cup of coffee and not a labor intensive process.

I bought one of these machines (Germans call them Moka) years ago and after some brief use it went into permanent basement storage. The problem? Absolutely no crema! My grandmother threw triple-ground espresso coffee into a (never washed) pan of boiling water, let it steep, and strained it into cups. This is identical to Cuban coffee, Turkish coffee, Arab coffee and Greek coffee. Some like it sweetened in the pan, but for good old paisano espresso (with crema), just treat it like machine-brewed espresso.
Hi Justine,
Yes, the stove top stuff is not true espresso (with crema). Rather, stovetop espresso is more akin to a stronger cup of drip style coffee.
Proper espresso can only be made with the right equipment, coffee bean and grind, etc.
Thanks,
Vince