You should plug your vertex colors into the color input of your shader.

1. With your object selected, add a new material:

![enter image description here][1]

2. Create a meaningful name for the new material. Next, open a node editor window. One way to do this is to create a new UI window by dragging up the triangle in the bottom-left of an existing widow:

![enter image description here][2]

You can change the type of your new window with the button on the bottom-left -- select "Node Editor"

![enter image description here][3]

![enter image description here][4]

Unfortunately, you have to type the _name_ of your vertex color layer into the Attribute node. This is accessible from the _Vertex Color_ section of the _Object Data_ tab in the _Properties_ panel:

![enter image description here][5]


  [1]: https://i.sstatic.net/DDioC.png
  [2]: https://i.sstatic.net/DtFiz.png
  [3]: https://i.sstatic.net/26e19.png
  [4]: https://i.sstatic.net/cjlRu.png
  [5]: https://i.sstatic.net/PlyhN.png