You hard boil some eggs, then mash them up to a fine crumble (add a bit of dry commercial eggfood mix, or some cornmeal to make it a bit dry). Also mash up the eggshells as fine as you can and add that to the mashed egg. This is about the best thing you can feed a bird... it's got all the protein they need.
You can also add some very finely chopped up veggies such as broccoli florets, to the egg, if you want.
If you can get coco fibres for nesting material they will love it, also some small white feathers, or some meadow grass hay. Also some folks on here use those little cotton puffs that people use for make up, and tear them up into smaller pieces. Finches seem to like the lighter stuff to line the bottom of the nest.