As these games usually begin, April has been kidnapped. Your goal in area 1 is to rescue her. This area has six distinct levels, but you need to go through only three. First, be wary of the Roller Cars: they can steamroll over you and that's not good.
The first sewer entrance you find is linked to the second sewer entrance further on, and there is nothing interesting in that level except a slice of pizza at the very end (if you want it, just use the second entrance).
So walk around the first entrance, around the building, carefully avoiding the Roller Cars. You'll soon come across another sewer entrance; this is the exit from the first sewer entrance. The third sewer entrance is the one you're interested in, because it takes you across the water to the other side.
Mousers creep across the floor, annoying bug things fly in the sky, and a couple foot soldiers. Nothing too unusual. At the end you will find the first miniboss, Bebop.
You will likely want to defeat Bebop using Donatello, since the bo is very powerful. Rocksteady appears with April, holding her hostage, at the exit. Do not jump up to them or Rocksteady will injure you. Bebop will generally charge at you, occasionally pausing to throw a few punches. The punches have limited range and only attack directly forward. Don't accidentally trap yourself on the left side, an especially easy mistake in the NES version because you start to the right of Bebop instead of the left, as in other versions. Even if you do get trapped, keep jumping and thrusting downward with your bo. After you exit, you will find a building with an open entrance; ignore this. You will then find two sewer openings: one is stuck between a building and the water, which is the one you want, since the other is a dead end.
There's a slice of pizza at the beginning, a perfect opportunity to replenish everybody's health in the NES version.
You'll reach the end with few problems. In the NES version, you'll encounter a miniboss. This miniboss is a regular enemy (later in the game) and should give you no trouble. None of these minibosses are in other versions of the game, but they're littered throughout the NES version. After you reach the exit, you'll find a building, inside which are Rocksteady and April.
The bottom storey has conveyor belts, but they should not present major difficulty. You have not seen the enemies here before and they're slightly stronger than usual (they're normally area 4 enemies). You may want to switch to Donatello, but you'll only have to get through a few of these enemies. After you go up the ladder, you'll find a couple more bad guys, then a mass of crates to your left. Rocksteady lies just beyond them.
Rocksteady is not difficult to defeat with Donatello. In the NES version, you can use the cheap trick of standing on the edge of the crates, kneeling, and repeatedly thrusting downward. Rocksteady will occasionally make a small hop right into the bo; just repeat this over and over to defeat him. In the Atari ST version, you cannot use this trick because the crates are scrolled off the left edge of the screen, which also means you cannot use the crates as a safe area. The Atari ST version is especially troublesome because Rocksteady can shoot in midair. Do your best to jump over his fire and avoid him when he jumps after you. Stay off the ground, and keep moving, striking whenever he's in range.