Psalm 149:4
⁴ For the Lord takes pleasure in His people;
He will beautify the humble with salvation.

God loves humility.  Humility is what He is like (Ps 113:6, Phil 2:8), and it is when we humble ourselves that we are most who He made us to be - most living in His image.

Micah wrote that humility is one of three things that God requires of human beings (Micah 6:8).  Isaiah wrote that God dwells with and looks to humble and contrite ones in a special way (Isaiah 57:15, 66:1-2).  The Psalmists wrote that the meek would inherit the earth (Ps 37:11), and that when Jesus returned, He would ride to victory on behalf of humility (Ps 45:4).

God resists the proud, but He gives grace to the humble (Prov 3:34, 1 Pet 5:5).  Therefore, Peter says, "Humble yourselves!" (1 Pet 5:6-7)  God will exalt those who humble themselves.  We have good reason to believe that this is true - after all, the Man who humbled Himself more than any other in human history has been more highly exalted than any other ever has been or ever will be! (Phil 2:9-11)

With all of that said, it must be noted that humility does not come naturally.  Pride and self-exaltation are very close to the root of our fallen nature.  It requires profound trust in God to humble ourselves completely and trust in Him to lift us up. 

So how do we begin?  We begin the same way we begin to pursue any virtue in the Kingdom of God.  We recognize that this virtue originates from and describes God Himself.  We acknowledge that this virtue is preeminently displayed in the person of Jesus Christ (Matt 11:29).  And then we meditate on the Man Jesus Christ and ask the Holy Spirit to grow the character of Christ in us.  It's His job after all.

For further study, check out Andrew Murray's book Humility. (highly recommended!)