When using improvise to cast a spell with {X} in its cost, first choose the value for X. That choice, plus any cost increases or decreases, will determine the spell's total cost. Then you can tap artifacts you control to help pay that cost. For example, if you activate the last ability of Archway of Innovation and then cast Wrath of the Skies (a spell with mana cost {X}{W}{W}), choosing 3 as the value of X, the total cost is {3}{W}{W}. If you tap two artifacts, you'll have to pay {1}{W}{W}.