The best way I believe is to put them in front of the board and explain that pawns are so brave they only move forward and never move back. If they know the other pawns are his/her opponent's they would understand they move towards them as it's they opponents forward.
The trickier part would be to explain how the pawns eat. I may say that they eat looking left with their left arm, and looking right with their right arm, but never with both at the same time (which would be eating in front of them).
I would suggest at an early age to use didactic games like
PreChess. Not sure if that term exists in english, but in spanish we have
You can find nice
PreChessgames within http://www.ajedrezparalaconvivencia.edu.uy/preajedrez/ , pity the web is only in spanish by now.
Specifically for practicing pawn moves I would suggest the "Pawn Race" and "Rescuing Snow White".
The clue with these kind of games is to play with less pieces and fewer rules involved. So the kid can focus on the pieces you want him/her to learn how to move.
Note: Just a note about ages. I started playing
PreChess games with my son when he was around three years old. He liked very much "searching for the treasure" which was eating pawns with a rook, one by one, trying to eat a pawn in each move. You would create a kind of labyrinth of pawns to eat.
Let me give some description in english so as you get what the games are about:
The aim of the game is to promote one pawn, which would be take one pawn to row 8 for White and row 1 for Black. Of course this game can end in a draw if nobody promotes a pawn.
It's a good game to practice moves and captures for pawns, and to explain the promotion of pawns.
Below you can see the initial set of the game:
The dwarfs (eight white pawns) need to rescue Snow White that was captured by the witches (two bishops and a horse).
The dwarfs can rescue Snow White if at leat one dwarf gets to the last row and then makes a final move to rescue her (bare in mind that this is not possible in chess. It's a modification to create this PreChess game). Once she is rescued White win the game.
It the witches capture all the pawns then the dwarfs can't rescue Snow White and Black win the game.
Below you can see the initial set for the game: