Russula* mushrooms are easy to identify to genus. They are usually all white, except for a colored skin on the cap that can be peeled off without otherwise damaging the mushroom. The flesh is white and brittle throughout--you can snap the stem or the cap and it breaks clean with an audible snap. They produce light colored spores (usually white) and the brittle white gills touch the stem. There is never a ring on the stem or a volva at the base; they are always mycorrhizal, sometimes with oak and other hardwoods, sometimes with pine forests.
Identifying them to species, unfortunately, is not so easy. Take this red-capped Russula. There are at least 70 species of Russula with red or pink colored caps in our area. Discerning them requires careful attention such details as the specific habitat, the mushroom's taste (always spit it out!), and then several microscopic features. It's a bit academic, as most Russulas are not sought out for any particular reason--they aren't considered great edibles, and at least some can make you pretty sick. Best to just appreciate their beauty, and the fact that they imply that the forest beneath your feet is a healthy web of roots and mycelium.
Also some people like to kick them, because they shatter into a million pieces.
And also this one was unusually small.
* "Reddish"