How do I purchase more iCloud storage via iTunes gift card

The process is automated, when you purchase the new storage it well ask to confirm your card information, but should charge any active account credit first.

See View your store credit in the App Store or iTunes Store - Apple Support and Buy more iCloud storage - Apple Support.

You should be able to pay for iCloud with a gift card, but you still require an active credit card on file. Basically when the gift card is on the account as a credit any purchases made are charged to the account credit first, once the account credit is zero then the credit card is used. The downside to using a gift card if you add it too soon it'll be used for App, Music, Movies, and other content purchases first. Currently there is no way too tell the system to use the account credit for one single purpose.

You can submit feedback about this here: Product Feedback - Apple

You should be able to pay for iCloud with a gift card, but you still require an active credit card on file.

If you have gift credit on your account profile, you may remove any credit card information listed there. You are not required to have a credit card on file if you have a credit balance.

How your iTunes Store, Mac App Store, App Store and iBooks Store purchases are billed to your iTunes Store account (Apple ID). -

http://support.apple.com/kb/HT5582

Payment is automatic. It will take from the gift card balance until that is used up, then will take from the credit card.