To worship God in a spiritual way is to worship him in the beauty of holiness. Worshipping God in holiness is the way every christian should follow in order to worship God in true religion. As christians, we must be opposite of the world, which means that our lives should be opposite of those who are not christians.
The book of Romans 12:1 teaches us to set ourselves as a living sacrifice, holy and acceptable unto God which is our real service. We should not be conformed by the world, we must abstain from earthly things and do the will of God. Our bodies is a temple of God and we must keep it holy always.
During the time of Israelites, they offer living animals as a way of worshipping God, but during our own time we no longer have to offer animal, instead what is required from us is to worship God in truth and holiness.
So as believers, let us live our lives as Christ. Keep our body holy and worship God in truth. Let the world know that we are christians by our works.
God bless you all