Fellowship is actively and consciously sharing something in common with another. A Christian can have fellowship with another Christian because they both have Christ as their Lord, Savior and their Life.
A Christian can have fellowship with God by being occupied with Christ. You must realize that God is Christ-centered. He has His sights on His Son. And if you are occupied with Him as God has Him in focus then both you and God have fellowship with each other in the person of Christ.