Everything has a logical place. If it doesn't have a home, it needs one, or it needs to begone.
Play this game with your kids often from little-hood: "Keep Or Toss?" You just super quickly hold things up and have them say "keep" or "toss" and all the "toss" things go into a box for donation/trash. Obviously you make sure they understand the rules first, LOL. Don't give them time to deliberate much, just ask them to give a gut reaction. Start playing this game with things like ripped pieces of art, toys that don't get played with, etc. As they grow they'll get to where they can do it themselves without fuss. I swear by it.
I would give the stuff a day or week to sit hidden somewhere in case they have serious second thoughts. In my experience, this is rare.
Also with kids it helps to have a distant younger cousin or two whom everything precious can be designated for. Then behind the scenes YOU decide what is really headed to said cousin and what is really headed for some other end.
For storage, especially toys, have containers that are appropriate sized and do not let them overflow. If they start to overflow, play Keep Or Toss. It is helpful to store things by categories -- the lego bin, the dolls bin, the blocks bin, the bookshelf, the jar of safety pins, the jar of rubber bands, the box of scrap paper, the basket of crayons. Etc. Books should not overflow their shelves. Either you need more shelves or less books, period.
If dresser drawers overflow, you either need less clothes or a new dresser. Pick one and do it.
Do not let things come into your home that aren't at least in the running as good-quality, useful/beautiful, sturdy, things that fit your life. If you have a kid who picks junk up at every free opportunity, limit how much can be kept and cull the collection (with the kid) often.
Give each kid a box that they can keep under their bed, in their room, or whatever. Could be a drawer. This is for all the random treasures and junk. Periodically play Keep Or Toss with the contents; if it overflows, it's time to declutter.
Broken things: fix, replace, or let go of...immediately, no question.
Keep superglue in your kitchen cupboard for instant fixes so stuff doesn't languish in the "fix someday" pile.
Think of how many of something you or your kids really need. Twelve stuffed bears? Would they be happy with three?
For entryways, have shelves or bins for shoes/boots, drawers for hats/mittens, hooks or hangers for coats.
For dirty laundry, put a basket or hamper in every place where dirty clothes usually get dropped on the floor. We have one in each bedroom and one in the front hallway. Empty and sort regularly into bins by the washer.
For trash and recycling, put a container in every place where people are likely to throw something away, and it won't end up on the floor. We have trash and recycling in every bedroom, the kitchen, the office, and the area where the kids do art. I also have compost bins where appropriate -- I even have one by the dryer to put lint wads in.
Keep stuff near where you use it. You might even get whisk brooms and dustpans for multiple areas of the house. I have four -- one in each bathroom, one in the laundry room, one in the kitchen.
Sets of storage tubs are your friends. Barring that, banana boxes from the supermarket work VERY well for basement/garage/shed storage if you do not have dampness or water in those places -- they are sturdy, and they have great lids.
Ask yourself, do I USE this, do I NEED this, do I LOVE this? If you can't answer yes to one of those questions, are you ABSOLUTELY SURE you will need or use it in the future? If you can't answer yes, get rid of it. Let it bless someone else's house. Donate to charity and get a tax receipt. Give to a friend who will need, use, or love it.
Remember, decluttering spreads just like clutter spreads.
Expect it to take years if you have a lot of stuff. Maybe it won't, but it always takes longer than you expect it will.
You might need to write out your mission statement -- the reason why you are decluttering, the reason why you want to do this. Post it on your fridge and remind yourself often.
Remember that love and memories live in you, NOT in your stuff!! Consider photographing anything you are attached to that is just sitting in storage that can't be used (like that picture you drew of your mother when you were five.)
Teach your kids that their art/craft projects are temporary, and put them up for a short time but take them down and replace with new ones and recycle the old ones. Photograph anything they are super attached to before recycling it -- as a last resort, if they are really hanging on. A few treasures can be framed, but embrace the rotating art gallery concept, and discard what's been enjoyed already. Don't worry, they'll make more.
When you need to replace things, try to replace them with a version that you love or that kind of coordinates with other things you have. Oddball stuff that doesn't fit a category or style can get weeded out over time.
Don't keep stuff that you know you only use once in awhile and know you can borrow from a friend or neighbor when you need it.
Take pride in what you decide to keep. Maintain it, care for it, display it. If something is not worth this effort, and it isn't something you NEED, get rid of it.
Clearing the stuff out of your house shifts the energy and newer, healthier, better stuff flows in. It's totally true.
Better to have one beloved version of something than a dozen "eh" versions of it. You only need one coffee mug.
With lots of kids, assign each a unique cup, bowl, and plate. Store them in the dish drainer; you or the kids wash them by hand after use, and drain, and then it's there for the next umpteenth snack. If you limit kids to water in their special cup, you won't have to wash it very often.
Simplifying helps with decluttering.
For us, one day a week is "clean up day"--things kind of build up over the week, and then we clean up all in one fell swoop on Thursdays. Somehow that works best for us. When the kids were small, we did it once a day, though their contribution was minimal. But the habit was created.
I love this phrase: "Pick your favorite." My kids have tons of hand-me-down hats and mittens, and they don't fit in our storage chest. Pick your two favorite hats and two favorite gloves (so there's a backup.) All the other ones will go to Cousin L.
Know when to throw stuff away. I used to get caught up in trying to match donations to the perfect recipient. No more. Taking a carload to the swap shop is easier than freecycling things one by one. Some things are in a condition that could borderline be used by someone creative who was desperate, but the chances of that person finding that thing are slim, and really they are just junk and need to be tossed out. A lot of thrift shops are picky, for a reason. Know what is trash so you don't waste your time.
Be patient with yourself and go slow if the project is big. Chip away at it. You'll get there. The trick is to send stuff out of your house faster than new stuff comes in. Good luck.
Back to add one more thing: It is not your fault that we live in a throwaway society and well-meaning people have bestowed clutter/stuff/junk on us over the years. Remember that the karma for throwing away junk rests on the person who first bought or made it, even if it gets tossed by your hand. It's not your fault you couldn't make use of Aunt Edna's broken plastic easter egg collection, and it's not bad that you accepted her gift with the love she needed to receive from that transaction. Toss them as a favor to her; you did not fail in not being able to make treasure out of her trash.
BUT---as much as possible, don't let people foist their trash on you unless you're willing to throw it away or rehome it for them.
When someone gives you a gift, it's yours to do what you like with. You have no obligation to use or love it. Feel free to bless someone else with it, or help a cause by donating it to a charity store. Inherent in every gift is the possibility that it isn't right for you, but you always get to keep the love that was attached to the gift.
Whew. I have had quite a journey! Still decluttering my XH's stuff from our divorce, and some things of my own as well. It really does take time, like peeling the layers of an onion, but trust that baby steps will add up.