Super Mario World/Star World 2

The two ways to complete this level are:

Race to the exit
Swim all the way through the level, avoiding any fish that might try to touch you. You can swim up and over everything (go outside of the screen's boundary) until the green tube and then decide if you want to take the normal or secret exit. Enter the green tube at the very end to complete the level. It's as easy as that!

In order to proceed on the Star Road, you will need to find the lock and key.

A Starman falls down at the beginning of the stage. If the Baby Blue Yoshi eats the star, he becomes an adult instantly, as opposed to making him eat 5 enemies. This is a nice little time-saver that will get you a quick, easy Blue Yoshi if you need one for a tough level.
 * Using the Starmen

Alternatively, you can just get the Starman yourself and plow yourself into the Cheep Cheeps, killing them, eventually getting extra lives. Move quickly if you decide to do this, you can get an extra Starman to extend the effect a little later in the level in a question box (the box will contain a single coin otherwise).

Secret exit
Instead of entering the green tube though, swim along the path underneath it. This is much easier if you've got a Yoshi who can eat up all of the fish that would normally chase you. At the end of the path, you will find the key and the lock!