This was the way my mom taught my sister to love broccoli when she and I were little, so I know I love it :-)
Take a normal-sized pot and fill it with water. Place it on the stove and turn on the flames. Take your broccoli and cut it into smaller florets. When the water is steadily boiling, quickly drop the broccoli in. Let it boil for about 30 seconds, then turn off the heat. Leave the broccoli in the hot (but NOT boiling anymore) water for about 5 to 10 minutes until it is almost cooked enough to eat but still a little crunchy. Make sure to push the tops of the broccoli in occasionally so it all cooks evenly. After its finished, drain the water out.
Place a large pan on the stove and put enough olive oil to thinly coat the bottom. Crush your garlic (I like a lot, but 2 should suffice if you're not as big of a fan). Place the crushed garlic into the oil and turn on the heat. Stir olive oil and garlic for about 2-3 minutes until the whole skillet is hot, then add the broccoli. Saute the broccoli for 3 to 5 minutes, then plate.
This way of cooking broccoli leaves it still a little crisp and not mushy. It makes a good side dish with pasta and the like :-)