Understand the insurance policy well. There are situations where, after the occurrance of damage to the aircraft, and a resulting claim, the insurer might ask you to defend yourself against the claim, (like saying it was not your fault, so the insurance does not have to pay). This can put you in the position where you have to be at odds with the person who lent you the plane, where you would rather see them having the claim paid out with no hassles. Being named on the insurance should take care of this.
Make sure that you know the deducable, so you are prepared to pay that amount. It may be payable even in the case of a total loss claim.
Best to do some flying with the owner, so you see how he/she likes to have the plane flown; power settings & leaning, shock cooling, procedures, how it is to be tied down and secured.
Have fun...