How would I add dots to the texture on a 3d object? I am pretty new to blender and I've been trying for a little while to get dots on a 3d surface. 

On the picture below you can probably better see what I am after. On the top is the image I am trying to recreate, and I am wondering how I can get that dot pattern onto my model. My model does have a bool and subdivision modifier, and I feel like that is making it a bit harder. I have tried following this (Procedural polka dot pattern with cycles), but I cannot get it to work on my model. I've also tried texturing, but I don't know how that works too well and the dots just get stretched out.

Does anyone have any suggestions?
I like your way of thinking, but the procedural texture you picked is meant to be used on a 2-dimensional plane. The z-scale isn't being touched at all by the other nodes.

While i cannot give you a setup for a procedural texure, why not create a small .jpg or .png and then scale up the UV map? You may have to mark the seams manually to get it lined up perfectly though. If you're using Smart UV, make sure "Stretch to UV Bounds" is deselected to not mess up the aspect ratio.