Procedure and method are very similar, but method is a smaller part of the procedure. Think of it in this terms:
In business, you have a plan. A series of steps, or a program, which must be followed to to accomplish a goal. A procedure is a smaller part of that program. It is how you execute certain steps. If step three calls for hiring a human resource director, than there will be a procedure which outlines how to get that done.
Method is even smaller. It is the step-by-step plan that you will follow to accomplish the procedure, which you are following to accomplish a subgoal of the whole plan.
Look at this definition from the business glossary:
Procedure: a subroutine ; a smaller program that is part of a main program. The procedure is executed when the main program calls it.
Procedures eliminate the need to program the same thing more than once. If you know that one task will be performed more than once in your program, it is better to write a procedure to handle the task rather than duplicate the program code when the task is needed again. Also, a large program is easier to understand if it consists of procedures, each with a well-defined purpose.
Here is the definition for method:
A process by which a task is completed; a way of doing something; The implementation of an operation.