Instrumental case - narzędnik

The instrumental case is used after conjugations of być.  Like:

Jestem Anglikiem - I'm an Englishman

Jest kotem - it's a cat

Jesteś Polakiem? - You're a Polack?

and just as I began to think all instrumental endings were -em:

Jestem farmaceutą / farmaceutką - I'm a pharmacist (male/female)

After the following prepositions:

nad - above

pod - below

przed - in front of

za - behind

między ... a ... - in between ... and ...

z - with

NB: if nad, pod or przed are used with a verb of motion, then the accusative case is used instead.

The instrumental case is used when stating mode of transport.  Like:

Jeżdżę do pracy samochodem.  I go to work by car.

NB: samochód (car) is the mode of transport, so is in the instrumental case, samochodem; 

praca (work) follows the preposition, do, in expressing motion, so is in the accusative case, pracy.

The instrumental case, as I guess the name suggests, is used in expressing what tool, or instrument, you are using to perform an action.  Like:

Nie robię pierogów z foremką / maszynką do pierogów - I don't make pierogi with a mold / pirogi press.

NB: pirogi is used in the genitive case, pirogów, as the direct object of a negative verb and following do (used to describe what the maszynka (gizmo) is for