For version 2.8

Use the render properties section of the scene editor.

[![enter image description here][1]][1]

There you can find the options that are available in your particular version.

[![enter image description here][2]][2]

For versions up to 2.79, you need to be on the info window

![enter image description here][3]

then select your render engine

![enter image description here][4]

**Note that blender internal and the game engine have been removed starting with version 2.8.**


  [1]: https://i.sstatic.net/N7803.png
  [2]: https://i.sstatic.net/9ATN9.png
  [3]: https://i.sstatic.net/H3sUl.png
  [4]: https://i.sstatic.net/wiWRh.png