Dots/Pattern/Texture

[BenSCR]

How can I make bacground dots/pattern/texture like in the middle of this illustration of a games controller and the 'Red, White and Blue' object on the thumbs.

[Monika Gause]

That looks like a pattern fill. https://helpx.adobe.com/illustrator/how-to/create-apply-patterns.html

[Ton Frederiks]

Add one of the patterns found in Swatches Panel > Open Swatch Library > Patterns > Basic Graphics > Basic Graphics_Dots and play with the opacity.

[Jeff Witchel, ACI]

You could also set up your own custom Pattern. Here's a link to a video turorial: Patterns