Trim the beef of excess fat and sprinkle with salt and pepper. Over medium-high, heat enough vegetable oil to nicely coat the bottom of a large, heavy skillet. When it is searingly hot, brown the steak for 1 to 2 minutes on each side; for cuts like skirt, be careful not to cook past medium-rare. Remove to a wire rack set over a plate and keep warm in a low oven; reduce the heat under the skillet to medium.
Add the onion to the skillet and cook, stirring frequently, until a deep golden-brown, about 10 minutes. Stir in the garlic and cook 2 minutes longer.
Cut the meat into thin strips (across the grain, for skirt steak); for tougher cuts of meat, cut into 1/2-inch pieces. When the onion mixture is ready, add the beef to the skillet and stir until heated through. Season with salt and serve in a deep, warm bowl.
If you sear the meat in a hot pan, you'll get a nice flavor and a good crust; if the pan isn't hot, you'll find pale meat simmering in its juices.
The Mexican bisteces often used in this preparation are taken from the tougher cuts (frequently the round) and pounded. Choose thin round steaks (often sold as breakfast steaks, sandwich steaks, flip steaks, wafer steaks or perhaps under other names) and pound them if necessary; or choose any thin steak tender enough to pan-fry. I like trimmed skirt steak because of its flavor and texture. Frequently, Mexican street vendors use the sheets of Thin Sliced Beef (Cecina); it's tougher, so they chop it into small pieces.
Minor Variations on the Theme: The meat may be marinated. It may also be fried in olive oil. Red onions may replace white, 4 roasted cloves of garlic could be used instead of raw ones. And strips of just about any roasted and peeled chile could be stirred in with the meat.