Does not increase the mana cost of the spell. It just requires a separate expenditure in order for it to succeed.
When this spell resolves, you either pay X mana or let your lands become tapped. The lands that become tapped are not "tapped for mana". If you choose to pay, you may pay the X mana using whatever mana abilities you want to use.
Only lands that actually have mana abilities will get tapped. This includes basic lands and lands with mana abilities printed on them, as well as lands which have been granted a mana ability by some effect.