To Bake a Texture in Blender 2.8, you need to first make sure that you’re using the Cycles rendering engine with your CPU, as Baking in Eevee or with a GPU is not yet available.
First off, the method I’ll be explaining will be slightly different if you’ve Painted your texture.
To start, select the object which you’d like to bake your textures to, (if you have a group of objects that you’d like to all be baked onto a single map, make sure to Join them together with Ctrl-J).
Next, go to the Shading Tab, and press Shift-A to add in an Image Texture node (but don’t connect the node to anything). Click New on the Image Texture node and name the Image whatever you’d like. Next, type in the resolution you would like your texture to be baked in—the default is 1K.
After you’ve named your new Image, with the object still selected in your Viewport, go to the Render Settings Tab, and click the drop down that says Bake. In there, you’ll select which maps you would like to bake (i.e Diffuse, Glossy, or Normal).
Once you’ve selected the map you’d like to bake, set the Output Margin, which controls the amount of “bleed” over each UV Map Island. The default margin is 16, but I would avoid going too low, unless you have a very “tight” texture at the edges.
After that, simply press Bake. Once the bake is complete, a good way to test if it worked is to Duplicate your original object, move it to the side, create a new material and use the newly baked texture as an Image Texture Node.
I’ve included a quick screen capture which shows me baking a Normal Map for a simple cube with a little extrusion cut into it.