If you're inexperienced at it, Super Mario Bros. 3 is a tough game, made worse by the fact that after you lose your meager 5 lives all the progress you made in each World is negated, and you have to do it over again.
So, like a lot of games, it's very helpful to throw more lives at the problem.
My favorite spot to do that is in World 3-9.
First, stomp on the Koopa Paratroopa and grab its shell.
Then run over to the right, being very careful not to hit the Goomba or the Bob-Omb that's hiding over there. Make your way to the Bullet Bill cannon and kick the shell over to the other side of it.
Then quickly make your way to the platform above.
And wait.
Bullet Bills will continuously be fired from both of the cannons, and the ricocheting shell will take out each one.
Until eventually
1UPs! And you can stand there in safety until the time runs out, which will cost you one life, but you've got plenty to burn at this point.
And, if you're playing a two-player game, it's good form to allow the second player the chance to do this trick also, so that you both have a ton of lives to play around with.