Complete the game twice in a row, and after winning the second time keep pressing the A button to active Stage Select. Each additional press of the A button advances the level you can start in.
To access the coins and pipes at very the top of Stage 1-3, you need to activate two secret elevators.
One is can be found at the start of the start of the stage, where you must position Mario exactly three "blocks" away from the left side the screen. Then simply jump and you'll automatically activate the elevator which will take you straight through the top of the stage.
The next elevator can found after defeating the second lion and dodging the two falling stones. Look for a row of five blocks that form a pattern with coins and bricks. Break the second brick with as Super or Superball Mario, then jump through the hole and the elevator will automatically take you up to the top of the stage where you will gain access to a secret pipe. Watch out for another plant enemy here if you're playing in Expert Mode.
In Stage 2-2, look for a vertical tower of coins near a pipe and Nokobon. There are two levels just ahead which seem out of reach, but there is actually an invisible platform you can walk across that will lead to the lower platform. You can only walk across it as Small Mario however, so first take a hit if you're Super or Superball Mario.
Complete the game once, then start a new game to play on a harder setting. Things such as more enemies and traps are present now. The cursor on the title screen will change into a Mario head to signify that hard mode is active.
Complete the game again on this hard setting to access a level select.
Note that since Super Mario Land has no save system that both of these extras will be lost when the game is turned off, so the unlock conditions must be met again to access them anytime you turn the game on.