You'll probably recognize many of these on sight, because they really do often look like little bird's nests. You can also expect to find a lot of empty nests which persist for a long time. Up to 1cm in size unless otherwise stated. All are saprophytic. One interesting way the spores are dispersed is by a raindrop that falls into the nest and splashes the eggs out.
All of these, with the exception of Sphaerobolus, are most closely related to gilled mushrooms, in particular they belong to the family Agaricaceae - with Agaricus and Lepiota, if you can believe that. Along with the discovery that most puffballs and earthballs are also in this family, this counts as the most remarkable shock of all time to come out of mushroom DNA studies.
You might find the various species on wood, sticks or soil.
Nidula - our most common genus. Recognized by shaggy white and brown colours. The eggs are imbedded in a gel when young without a cord.
Crucibulum crucibuliforme - resembles Nidula candida with its pale brownish eggs embedded in a gel when young, but this species sometimes has more yellowish colours when young and is velvety rather than shaggy. Each egg is usually attached at first to the nest by a small cord, so you can sometimes take a pair of tweezers and try to remove an "egg" to find out which genus you have. (Cyathus usually has a long cord).
Cyathus - the eggs are usually attached by a long cord and the eggs are blackish or greyish, not brownish.
Cyathus striatus - the interior of the cup is striate! Some here still have lids. Usually on sticks.
Nidularia deformis (farcta)/
There are probably too few species here to justify making a specialized field guide.