Always be sure to obtain permission if you don't own the property. Even public property - parks, etc - can be restricted in some areas. It never hurts to ask!
I've even gotten into the habit of getting signed permission from home/land owners. I have a "standard" no-fault release for owners to grant me permission to be on their property and that I will not hold them liable for injury. Also, it states that I will close gates that are closed, will remove trash that I find, will fill in holes, etc - basically, that I will leave things they way they are or BETTER when I leave. Having a signed form works well when law enforcement approaches you due to a concerned neighbor, when another family member approaches you, etc.
I also always try to stop bye when I am leaving to show them what I found. I offer any "personally identifiable" items, such as jewelry with names/initials in them, to the owner in case it is a lost family item. Although I have only been at this for a year, I have never had anyone want to keep a nice "un-identifiable" item, such as an old coin. My feeling is, treat the owner well and you will get to come back anytime you want! Sort of like prospecting or fishing! They will be glad to see you!
Best of luck,
Lookin