Imagine two poeple pushing on a cart at once.  The cart moves in a direction that is determined by BOTH of the pushes.

In this animation, the orange arrows show the pushes on the cart, the blue arrows are copies of the orange arrows drawn from the ends of each other, and the pink arrow is called the RESULTANT.
I call this method of vector resolution the "graph method" because you can usually get decent results if you are pretty careful when you draw.  You need graph paper and a protractor.

Here is a site that uses a program to show you the process.  You use the mouse to create any 2 vectors and the program draws the resultant.
Login to Lecture OnLine. In the 2D motion chapter, solve: Graph Method 1 and Graph Method 2