por and para can both translate as for in English. However, they are used differently.

Por can also often be translated as by. It is used in the following ways:

mathematics
porciento - percent; 4 por 2 - 4 by 2

time
estaba por tres horas - he was here for three hours

motion
venimos por tren - we came by train

and support
estoy por la paz - I'm for peace.

Para, in most circumstances, can be translated as in order to. It is used in the following ways:

implying a purpose.
Estudio para tener exito - I study in order to have success.

referencing a destination
Se va para Argentina - She's going to Argentina.

You can also check the prepositions lessons for more information.