This is not a mushroom ID site!
This is me romping around in the woods and taking pictures, and telling you what I think I've learned.
I take a lot of pictures. It's common practice to pick one specimen and lay it, gills facing you, next to a standing one, so you get most of the major features in one shot--like this. Slice one in half, too, while you're at it--like this. The texture of the stem interior is an important diagnostic feature--solid, hollow, stringy, etc. Some mushrooms bruise or blush when damaged (which may take up to an hour) and that color is another identification feature. Also, there are often key diagnostic features below the soil line, so use your pocket knife to dig the specimen up, instead of pulling it (a Xeruloid mushroom I once found had a "root" about a foot long!). And with Amanitas especially, it's all about that base.
Take note of where it was growing, for example near conifers or hardwood, dead or live wood, from the ground, on a log, in moss. Then crack open a field guide (can't have too many of those, as it turns out), find something that looks very much like it, and actually read the description, which is when you realize you should have collected a specimen to bring home because of some detail you didn't notice in the field. You can't take a picture of the odor. In the field, dig it up to see any underground structure, sniff it, cut it in half to see the inside of the stem, see if it bruises, take more pictures, etc. If you find a mushroom in oak woods, but the description you're reading says it's only found in conifer bogs, it's not what you thought it was.
I used to not collect specimens, because I am a slacker, but I've changed my ways. Now I bring a stack of wax paper sandwich bags and a Sharpie and write notes directly on the bag. On a long hike when there's lots of mushrooms, it's easy to forget details.
Don't forget to sniff it! To get the full effect, pinch off a piece of the cap and crush it in your fingers, then smell it. The smell can be surprising, and is noted in field guides (raw potato, bleach, cucumber...). We were hiking once and a friend found a kind of boring-looking tan mushroom. He examined it for a minute, then handed it to me and said, "Smell this." If I had my eyes closed I would have sworn it was a jasmine flower. Astonishing! Took a while to ID it, the books weren't describing the smell as being sweet and floral (we did see "swamp gas" and "coal tar," though). He finally found one older text that described it as "odor of jessamine." Nailed it! It was Tricholoma odorum.
Sometimes the final, specific ID feature you need comes down to the color of the spores, which is when I (used to) swear a little because I didn't collect a specimen. So, you should collect a specimen, and make a spore print. You do this to see the color of the spores. There are many mushrooms that might fit each other's general description, but the color of the spores will be the clincher. Some of the best resources start the ID key with spore color, so if want to use them, you'll need a spore print. Plus, it's fun having little science experiments around the house--makes me feel like a kid again, before Adult Concerns kicked in. But, that's just me.
Sometimes by the time I get a mushroom home in its little wax paper bag it will have dropped enough spores to see the color clearly.
Anyway, first I find what seems like a match in a field guide. I started with the National Audubon Society Field Guide to North American Mushrooms, by Gary Lincoff--it's arranged by general morphology (gilled with a ring, puffball, branched, etc.), then grouped by size and color, so it's pretty easy to land on something that looks like a match. Then, I actually read the description. If you hit a term you don't understand, check the glossary, or look for examples online. After a while you'll start to recognize the genus, so you won't have to look through all the pictures--you'll be able to go directly to the sections on boletes or ink caps, for example.
If it seems like a match (after actually reading the description), I cross-reference it by looking it up in other books, trying hard not to force it to fit (if you don't have multiple field guides, do not despair. There are some very good online options. Read on).
Then I type the name into a search bar, compare images all over the web, think maybe it really is a match, and then go to legitimate, educational websites for even further detail (see "Choice links" at left, and more below).
Do be aware that anybody can put a mushroom picture online and slap a name on it, so pay attention to who the author is. I've seen some honking erroneous IDs on Flickr and elsewhere online. I've made them too.
"Mushroom Expert" is my favorite online ID site. Once you think you know what you have, you can look up the species name on that site, and see clear, concise descriptions (and yet more pictures). The author, Michael Kuo, has a sense of humor and a sense of perspective, as far as I can tell. He's funny. Here's a link to his page on "Identifying Mushrooms"
If you just can't find a match in a field guide or an online resource (some less common mushrooms don't make it into the most popular field guides), sometimes you can get there by typing a description in the search bar, like "slimy orange cap mushroom," or "red Missouri spring mushroom." Find pictures, read the description, and take it from there.
There's also lots of online mushroom-ID groups, poke around and find one you like. Post pictures, and people will help you. Bear in mind you may have no idea of the expertise level of who's replying, so take their ID suggestions with many grains of salt, and verify it for yourself. Be prepared for the usual online cross-section of humanity, including people ridiculing you for your ignorance, vicious fighting and name-calling, and bad information. It can be really insane. There are now lots of local mycological societies on Facebook, those seem to be generally less crazy than international mushroom forums with tens of thousands of members. Try searching "(your state) Mycological Society."
A word about field guides:
There isn't one book that includes all mushrooms. I don't think there's even one that includes them all for a single U.S. state.
There are estimates of up to five million mushroom species worldwide. There are tens of thousands in North America, and thousands in the Midwest. The Audubon guide is a great first field guide, and includes over 700 of the more common N.A. ones, but sooner or later you're going to find something that isn't in it. Get more books. It's the only way. Get ALL the books! Get a second job so you can buy more field guides. There are books just on morels, one on nothing but N.A. boletes, one on nothing but eastern N.A. boletes (and it's just a thick as the other one), and books about edible mushrooms. Your interest (and frustration) level will tell you what you need. And never forget about libraries, which are full of books. If you find yourself checking the same one out several times, maybe it's time to break down and buy a nice used copy somewhere.
If you find a single, beautiful mushroom and feel bad about picking it just to identify it, then don't. I totally understand. I do this myself sometimes. The world will (probably) continue to spin on its axis, and that mushroom ID probably won't be critical to the world of science.
Sometimes the ID comes down to looking at the spores through a microscope, which I don't have, and then I swear some more. Mark my words, I'll get one one day.
But still, at the end of the day, I was out in the woods, inevitably found some natural marvel (I say, "What the hell is THAT?" a lot), and probably have some pleasing images I can foist on my friends, who have been very indulgent with me about all this.