Psalm 33:3 goes: "Sing to him a new song; play skillfully, and shout for joy".
There are three music-related activities that are described in this verse that we can offer to God. We often focus on the last part, 'shout for joy', in that singing in worship to God is the end result of our compositions, arrangements, practices and rehearsals. However, from the verse, these activities are in themselves an offering to God, and we must take them as seriously as we do for worship.
i) Sing to Him a New Song
I believe this refers to compositions we make. This allows us to offer God the results of our creativity, much like how a child might design a drawing for his or her parents. Our compositions are not only acts of creativity, but also personal acts, because we express what we want to say and feel, rather than what another songwriter felt and said before.
To me, creative arrangements of old songs also count under this category. This is because new arrangements inject new life and meaning into old songs, and like before also requires the arranger to offer his or her creative energies unto God.
ii) Play Skillfully
We can also play skillfully as an act of worship for God. Imagine that the president of your country has requested that you play your instrument for him, for perhaps an hour. You would definitely put loads of effort into practice. The same is required for God, except that God is infinitely more important than any person! An excellent God definitely requires our attitude of excellence, and no slipshod work should be permitted.
Also, practicing on our instrument requires a substantial amount of time and effort, and in this way we give our time, time that could be used for maybe computer games and hanging out with our friends, as a sacrifice to God.
I also did a search for the word 'skillfully' in the Bible, and it appears about 4 times only, in Exodus and Leviticus, primarily about weaving garments. In Exodus 28, the priests' waistband is supposed to be 'skillfully woven' (v. 8) in the manner the ephod (another garment) is woven - a garment made of gold, blue, purple and scarlet yarn, and finely twisted linen (v.6). Such a garment must indeed require long hours of effort (especially if your clothes had gold on them!), and years of apprenticeship and experience. As a musician for God, you must also be willing to put in such effort and time to play your best for God.
In summary, singing songs to God is not the only music-related action we can offer to Him; we can also offer our creative energies through personalised compositions and arrangements, as well as sacrifice our time and effort to play skillfully for Him.