How do I purchase more room for data on my phone

iCloud Storage will not provide more space on your device at all.

It will only provide space in iCloud on an Apple server somewhere for backups, iCloud Photo Library and files in the iCloud Drive portion of iCloud.

It will not increase the physical storage space on your iPhone.

click here ➜ What's the difference between device storage and iCloud storage? - Apple Support

Hi MichaelFrench,

Follow the steps in Upgrade to iCloud+ to update the amount of space you have for iCloud.

Also check out this YouTube video from Apple Support on the subject as well: How to upgrade and manage your iCloud storage on iPhone or iPad.

Take care.

Just might need to clarify that purchasing more storage space on iCloud will not increase the storage capacity on your phone. The storage on your phone is fixed. It cannot be increased, but you can gain more space by deleting other data on the phone.

Head to the settings app on your iPhone or iPad. Click on your name (on the top of the navigation page), then "iCloud > Manage Your Plan" and select the plan you want to upgrade to.