Using 2.8 and Cycles rendering here is a simple case that should correspond to your context:
An object with 3 materials with its own UV map (eventually several):
Each material here has its own associated mesh faces and the material look like this:
The node setting could be more complex, but that does not matter and I presume this part is already set up in your context.
Now we prepare the target on which we will bake:
Duplicate your object.
Remove the existing materials (these materials are from the original and we don't want it for the target). Use the '-' button to remove the materials.
Add a new material: use the '+' button and create a new one.
Create a new blank image, name it target and save it to disk (for some reason the bake won't work or not always if not saved, maybe because the image is considered as generated).
Create the UV map for this object: remove existing one (they are from the original mesh) and create a new one with the mean you need (smart uv project can work).
Prepare the node setting as show in the lower left part of the image above.
In particular, we need the UV map input and the image texture (with the target texture). You can already connect this texture to the shader. That will produce a warning when we'll bake but this is of no consequences in our context.
Once all this is prepared, place the two objects at the exact same location (and rotation, etc.) so that they overlap exactly.
Select the original and shift select the target. That could be a bit tricky as they overlap but pay attention to do it in this order: select one until the original is selected then shift select to have the target as selected active object.
Now we can bake:
Go to the bake section of Cycles settings:
I presume you want to have the original texture 'pure' colors with no shading (lights, shadows) effects. So choose 'diffuse' as bake type and choose 'color' as influence.
Choose 'selected to active' (all selected object will contribute to bake to the active one).
Choose 'clear image' (erase the image at the beginning of the bake).
Click the 'bake' button.
Here is the blend file so that you can check things. Textures are packed in it but you may need to save the target image to disk as said before.
Note: the target shader may fail to update automatically once the bake is done. Simply manually reactivate the node texture output to correct that.