If my grandmother left me money in the bank, how do I go about getting it?

This depends on several variables.  How did she leave for it you - in an ITF, POD, TOD or was the account joint.  Assuming you are of age, I would suggest going to the bank with a death certificate.  If she left it for under a will, then you will need to apply to the court for letters testamentary.  I would suggest that you try the death certificate.