When should you ask for a blessing? Generally your first encounter with the priest of that day, you should request a blessing. To do this, you dip your right hand down low to the ground, cup it in your left, palms up, and say, “Father, bless!” The priest will trace the sign of the cross on you with his fingers held so as to spell out “IC XC - Jesus Christ,” and will rest his hand in yours. At this point you kiss his hand, and that’s the blessing.
But why kiss his hand? Isn’t that yucky? No - the priest uses his right hand to consecrate the Body and Blood of Christ, to elevate the Lamb at “Holy Things are for the Holy!” and to perform all other priestly functions. You are showing respect for his office as well, and submission to the authority of the Church. If this sounds ever so slightly medieval to you, it is - it’s an ancient act of humility that other denominations have sadly forgotten along the way. We do something similar at the end of the Divine Liturgy when we approach to reverence the Cross. It’s traditional to kiss the feet of Christ, and if you haven’t received Holy Communion that day, to kiss the hand of the priest that prepared the Holy Communion so as to be connected to it somehow. If you have received that day, generally you do not kiss his hand also, unless you want to.