First, take the chicken across and leave it there...

you and the chicken >>

Go back alone...

<< you

Take the fox across...

you and the fox >>

Leave the fox and take the chicken back...

<< you and the chicken

Leave the chicken and take the corn across...

you and the corn >>

Leave the corn with the fox and go back alone...

<< you

Finally, take the chicken across...

you and chicken >>