Some things to remember are below:
Material scraps - It's a good idea to make sure that the material is cut thinly, and not too long, as short pieces can be more easily transported and woven into the nests.
Feathers - Birds use their own feathers to insulate their nests, so give them a helping hand by collecting any small feathers you can find and adding them to your dispenser?
Twigs - This may sound obvious, but twigs provide the basic structure of the nest. Short, thin twigs are best, strong enough not to snap but with some flexibility.

Some small birds apparently use spider silk in their nests, so making your garden a safe habitat for spiders can help attract birds of that kind. Many birds also use mud in the construction of their nests, so you might consider keeping a muddy puddle in your garden for them.

Some people use the fluff from tumble or spin dryers in their dispensers. It is not recommended because the lint dries out and crumbles once it's been rained on, meaning that nests built with it become unstable, and residues from detergents and fabric softeners can prove harmful.