What you're asking about is actually a pathfinding question; more specifically, it's the "any-angle pathfinding problem."
If you can limit the edges of obstacles to a grid, then a popular solution is to just use A* on that grid, then apply path-smoothing. However, there is a (rather recent) algorithm that is both simpler to implement/understand and gives better results than path-smoothing. It's called Theta*.
There is a nice article explaining Theta* (from which I stole the above image) here
If you can't restrict your obstacles to a grid, you'll have to generate a navigation mesh for your map:
There are many ways of doing this, of varying complexity; see for example here, here, or here. A quick google search also turns up plenty of libraries available to do this for you, such as this one or this one.
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