Does anyone know what to do with abandoned property and how long must you wait to do anything?
A very complicated question. You should talk to a lawyer for specific legal advice. But out of curiousity, what in blazes are you talking about?
In what way is the property abandoned?
Before any lawyer could answer such a question, the first thing they’d want to know is jurisdiction: what state or country is the real property situated in?
IANAL, of course.
Check title. See if it’s owned by the government.
Perhaps try to locate the owner and buy it.
A risky method for you to get title may be to squat on the property for a certain number of years and get title that way. Check to see what your state’s adverse possession period is. Oh, and call a lawyer.
It also helps to have some background on what you are trying to do with the property.
If you are a landlord and you are claiming the property was abandoned by a tenant, that’s a different story than if you are trying to acquire title to real property.
This is a landlord situation where personal property was left behind. Bedroom furniture, clothes, shoes, board games, etc, etc. I would like to know what to do with these things. Can I have a garage sale, throw everything out, donate to charity, or all of the above?
Here is a sem-recent thread in which we discussed this issue:
First we gotta define *abandoned. Lost property ain’t abandoned. Stolen property ain’t abandoned.
This is should be covered by Tenant/Landlord laws in your jurisdiction. Are you a landlord who is unfamiliar with the laws governing such? 
Check your state law.
Call an attorney in your jurisdiction.
In California, there are statutes dealing with this. I have no idea if or how these laws apply to your case.
Generally speaking and without addressing your particular case, if a lanldord believes a tenant has abandoned and rent is unpaid for a certain period of time, the landlord can deliver notices to the tenant to (1) confirm whether the tenant has indeed abandoned the residence; and (2) give the tenant a right to claim their personal property.
If the landlord gets no response, then there is an abandonment and the landlord can take possession of the premises and the stuff. If the stuff has enough value, the landlord must sell it and apply it to the rent. Otherwise, the landlord can do anything with it.
To determine if and how certain laws may apply to you, call an attorney.