While an octagon is technically any eight sided polygon, you’re probably thinking of a regular octagon; an octagon where all of the sides are the same length (ie, it’s the shape of a stop sign). These turn out to be very easy to draw once you have practiced your squares enough times.
You could draw them using angles, but honestly doing it that way is just over complicating things. Just follow the short instructions below for a super easy method of making an octagon.
How to draw an octagon without measuring angles:

First, draw a square. If you’re working against a grid, try and make it 3 by 3. 
Section all four sides of your square into thirds. If you made a 3 by 3 square on a grid, this is already done for you.  
Connect the marks to finish your octagon. 