An excellent sensible question at last!
I would suggest the answer is both, us and God. Our relationship with God is as a covenant, whereby we give ourselves to love and serve God, and God's part of the covenant is to provide us with a saviour - His son Yeshua, (Jesus) and through him and the gift of the Holy Spirit, as well as the other gifts such as wisdom and discernment, we are taught, directed, refined towards understanding the difference between good and evil.
It is through our experiences (through God's correction and refinement, through those experiences) that we acquire and learn to be holy. We also need to reject intentional sin and evil, desire holiness instead, -that is our part. God looks at the heart and its our desire towards Godliness (understanding God and the concept of purity as apposed to wickedness and evil) is the beginning of holiness!
Holiness is mix of many things, including spiritual maturity, obedience and willingness to 'stand alone' against evil and sin! Holiness is also a God given gift placed upon those chosen for a specific task i.e. Holy men of the Bible.
Therefore, God is able to produce Holiness in a person i.e. Saul became Paul through God's transformation- he became a Holy Man, who 'stood alone' for God!!!
Humans will never in their human form be able to acquire true holiness, as God is way beyond human righteousness, which is seen as 'dirty rags'. But we can achieve a level of righteousness that is acceptable to God, through Christ our savior which covers our sins so that we appear holy. However, when Yeshua returns again to collect us who belong to him, we will be transformed into holy sons and daughters of our Father God! Then and only then will we truly be holy! This applies also to Jews who have rejected Christ as their Messiah, they will also be made 'holy', God will remove the scales from their eyes and unblock their ears, and remove all sin from them for ever! Even the pots and pans in The Holy City will be made Holy!
Holy refers to pure, clean, unblemished, sanctified, without sin and consecrated - as was Adam and Eve before their temptation.