This passage needs to be compared to Ephesians 5:18-20 where it speaks of being filled with the Holy Spirit and the results of this is the same as in Colossians 3:16. So to sum it up, letting the Word of God control your life is the same as being filled with the Spirit. To dwell richly means the word is at home in your heart because we are not allowing our will to dominate, but His will and word. All of this results in the teaching of truth, and admonishing which is the warning against error. The rest speaks of using the word in the psalms and hymns and spiritual songs to do this which results in the joy and thankfulness spoken of that is a display of the filling of the Spirit. Being filled with the Spirit just means we let the word of God control all of our being in all we do and think. It is not something that causes craziness as some people believe. It results in God being shown in all areas of our life.
Colossians 3:16 Let the word of Christ richly dwell within you, with all wisdom teaching and admonishing one another with psalms and hymns and spiritual songs, singing with thankfulness in your hearts to God.