Euler's Method is a bunch of tangent line approximations stuck together. The basic idea is that you start with a differential equation and a point. You do a tangent line approximation to get a new point.
Then you use the new point to do another tangent line approximation.
You do this over and over until you get to the end (which will be specified in the problem). The catch is that, after the first tangent line, instead of drawing real tangent lines you'll be drawing pretend tangent lines. This will make more sense after a couple of examples.