May the grace of the Lord Jesus Christ, and the love of God, and the fellowship of the Holy Spirit be with you all. 2 Corinthians 13:14
Fellowship of the Spirit means more than just having a relationship that's friendly. Let's look at this verse --- Therefore if there is any consolation in Christ, if any comfort of love, if any fellowship of the Spirit, if any affection and mercy, fulfill my joy by being like-minded, having the same love, being of one accord, of one mind. (Philippians 2:1–2)
Since we all share the Holy Spirit, Paul is ending the letter asking the believers to have that fellowship be in all; We as believers all share that Holy Spirit and so we ought to be filled with it's love as well. Love and fellowship of the Spirit work together.
How can we apply this to our lives today, ask God to love others just as God loves us. We don't deserve his love and mercy yet he extends it to us freely.