Who can 'own' a wallet? I administer a public association. Can the association have a bitcoin wallet? Or does it have to a person that owns the wallet.
Any sort of entity can own a bitcoin wallet. Being a decentralized system, there are no rules in place saying what sort of persons or organizations can own bitcoins.

The simplest way to manage it would be to give the password to one or more trusted leaders of the association. This would mean that any of those leaders could spend (or steal) the funds at any time.

Another way would be to use a multi-signature address, so that some quorum (say, 4 out of 5 board members) of signatures is required. This would mean that your leaders must agree to spend (or steal) some amount of funds. You might generate this with, e.g. https://coinb.in/multisig/

You could have one of each: a "hot" wallet that anyone can spend from, for convenience, and a "cold" wallet that stores the bulk of your funds, but requires additional authorization to spend from.