There's a lot of donations boxes scattered all around my town from various projects for helping the homeless and poor. They've become common the last half decade. Don't remember seeing much before. Salvation army/churches are also a common donation choice in my area. Can also give or sell them to a thrift shop or flea market I guess. I prefer the donation boxes run by what at least seem to be non-church charities, personally. Been using 'em quite a bit cleaning out my house.
I just drop them off at the thrift store. If it's something that I think would really benefit someone less fortunate who couldn't afford it at the thrift store, then I put it on Craigslist or offerup. Offerup is annoying though, so I only use it for stuff that would appeal to a younger audience, since youngsters seem to want an app for everything, even things that work just fine as a website.
There are some local classified websites where you can post stuff for free and there are also multiple nearby thrift stores for second hand stuff that will sell things very cheaply for you if you waive your own part of the price.
Yup. I rarely buy anything nondisposable anymore. Get it free and give it away when I'm done. Especially good for kids' clothes, furniture, and electronics.