PS1 is a 501(c)(3) charitable institution, which means it can accept donations of money or things and the donor can claim a tax deduction.
The page for Tax Deductive Donation talks about the tax aspect.
For non-cash donations, though, the first order of business is finding out of the donation is wanted in the first place. Not everything offered for donation is wanted. A good inventory, a description of what you have to offer, including pictures and some assessment of the condition of the stuff, is helpful.
Someone at PS1 has to take responsibility for it and find space for it. Area Hosts have the ability to tell you if they will take responsibility for the thing and find a place for it, or you could contact the Board or both.
Generally, you should plan on making an appointment with whomever you will hand it off to, and drop it off with them at the space. If your person isn't able to meet you, then you shouldn't drop it off. Generally.
If what you has isn't tempting for an Area Host to add to an area, then you could post it to the public or private Google Groups and see if individual members or just anyone would like it. You're on your own for making the connection, but the good advice about not leaving it here without meeting your person still applies. You don't want to be the one who dumps unwanted, unclaimed things here and has to come and pick them up again.
Donations can be great, but they have to be wanted.