From the entrance to Brinstar, proceed right through several rooms. You'll eventually reach a large room with a red blast door to your right. Instead of trying to open it, look at the floor in the room just before this red door. There's a single, suspicious block on the ground. Shoot it with your Power Beam to reveal a hidden passage leading downwards. Drop into this passage.
Follow the path downwards and to the left. You'll enter a room with a few enemies. Continue left, and you'll find a small alcove containing your first Missile Tank. Collect it to gain 5 Missiles. Now you can open those red blast doors! Remember to press 'Select' to switch to Missiles and 'B' to fire them. With Missiles in hand, you can now backtrack and open the red door you encountered earlier, or continue exploring this lower section of Brinstar for more power-ups.