It is difficult to get lost in the first World, as your only option, typically, is to travel straight up. Right from the start, you can collect a Speed Potion. Then as you progress through the world, you will encounter, in order, a Power Rock, Hyper Bomb, a Rock Case, a Star Rock, an Artificial Heart, and finally, the boss of the world.
Get to know how the enemies move, and learn how to attack them safely. Screens where helicopters appear are a good opportunity to regain health by positioning King Kong in a safe location, and attacking each helicopter as they approach. Sometimes, two helicopters will appear on top of one another, so punch continuously as you begin to hit them so that the second helicopter doesn't damage you.
The boss of World 1 is a gigantic shellfish. It attacks by sending out many smaller shellfish minions. It is best to toss rocks at it as it approaches. It is not a very strong boss, so it should be easily defeated.
Once the boss is defeated, you should return south to the warp zone that leads to World 2.