In this stage, you are defending three rows from the crazed zombies that want to gain access to your house and eat your brains. The lawn mowers on the far left side of the screen will mow down one set of zombies should they get through your defenses (or if you have no defenses), and then that row will now be vulnerable to any invading undead.
I always leave the first two columns empty, and that is where I place all my Sunflowers for the game. Three Sunflowers will make more than enough sun for you to beat level 1-2, but I usually go ahead and put down six. You want to put down two as fast as you can in the same row, and you should be able to do that before any zombies show up. Then, keep collecting sun until you hear the first zombies show up. If you
have 150 suns at this point, you can go ahead and put another Sunflower down in a new row. As soon as the first zombie shows up, plop a Peashooter down in row 3. The Peashooter will be able to destroy any zombie as long as you have not waited until it is already in row 5. Keep collecting sun and put another Sunflower in the same row as your third one. At this point, simply put down a Peashooter whenever you can afford one and make sure that all your rows have at least one peashooter. The zombies are all weak at this point, so you should be able to defeat them easily.
At the end of stage 1-2, you will receive the Cherry Bomb. A Cherry Bomb will blow up anything in all the blocks surrounding the block where you plant it. It costs 150 suns and can save you in a pinch.