If you find as the game progresses that you are unable to access a needed resource because it is located in another player's territory, do the following.

Build a city on the opposing city's border immediately adjacent to the desired resource.

As quickly as possible, build culture-increasing improvements in the new city (temple, library, cathedral, etc.).

Your new city's area of influence will expand, eventually encompassing the desired recource, and possibly causing the other city to defect to your side.

In either case, the resource is now yours.