In situations/languages where you have access to both of these constructs, the general divide is as follows:
- If the request is for something the object has, use a property (or a field).
- If the request is for the result of something the object does, use a method.
A little more specifically, a property is to be used to access, in read and/or write fashion, a data member that is (for consuming purposes) owned by the object exposing the property. Properties are better than fields because the data doesn't have to exist in persistent form all the time (they allow you to be "lazy" about calculation or retrieval of this data value), and they're better than methods for this purpose because you can still use them in code as if they were public fields.
Properties should not, however, result in side effects (with the possible, understandable exception of setting a variable meant to persist the value being returned, avoiding expensive recalculation of a value needed many times); they should, all other things being equal, return a deterministic result (so NextRandomNumber is a bad conceptual choice for a property) and the calculation should not result in the alteration of any state data that would affect other calculations (for instance, getting PropertyA and PropertyB in that order should not return any different result than getting PropertyB and then PropertyA).
A method, OTOH, is conceptually understood as performing some operation and returning the result; in short, it does something, which may extend beyond the scope of computing a return value. Methods, therefore, are to be used when an operation that returns a value has additional side effects. The return value may still be the result of some calculation, but the method may have computed it non-deterministically (GetNextRandomNumber()), or the returned data is in the form of a unique instance of an object, and calling the method again produces a different instance even if it may have the same data (GetCurrentStatus()), or the method may alter state data such that doing exactly the same thing twice in a row produces different results (EncryptDataBlock(); many encryption ciphers work this way by design to ensure encrypting the same data twice in a row produces different ciphertexts).