What about our lives and words "hallows" the name of our Father?
As a Christian I bear the name of Christ. I'm to reflect Him in all that I do. I "hallow" His name as I give others a glimpse, a fragance of Him.
What desecrates and besmirches it?
Sometimes, by word, actions and re-actions Christian's stink; they reveal to the world their selfishness and unloving spirit, and that is a descration of the holiness of the Father's name.
How should we "hallow" the Father when we begin to pray?
The more we come to know our Father the more we will see and understand Him as holy. I hallow His name when I pray by recognising, and maybe even, thinking and reciting verbally, who He is, and also, in seeing my own lowliness in relation to His holiness.