Next easily observable part is the stipe or stalk.
Again shape and size can give directions. Is it robust, or maybe flimsy? Thicker at the base? How about the color? White, red, brown, or something else? The texture is scaly like a snake's skin, or smooth, perhaps covered in hairs?
How about the remnants of veils? The annulus around the stalk like a ring or collar. It can take variety of looks, can be droopy, thin, some has considerable density. How high is it on the stem? Beware on some mushrooms with time they can disappear with age. They also can leave behind a light spore print, most of the time very hard to see, but can be significant when id. How about the remnants of the universal veil - we noted them when talked about the caps -, the volva at the base of the stipe. If you can't see it, that doesn't mean it isn't there...
So now we should remove specimen. Gently not to make some important traits disappear. It's better to remove it in full them cut the stipe so we can see what's going on below the fallen leaves or grass or maybe even the soil covering the base. Now we really can see if it has a volva or not.
There is a third type of veil, the cortina, it is the same place where the annulus should be and resembles to spider web, and it's strains between the edge of the cup and the stipe.
And a fourth veil is a variation of the universal veil, which basically a slime covering the whole mushrooms. I doubt I would pick one looks like that. Are those species even edible?
Anyway we should take a look at the base again after we removed from the soil, because the roots, called rhizomorphs, or more simply rhizomes, also a trait that can help id.
And again just like the cap, does it bruise? Poke it, cut it, and watch of discoloration.