How do I free up space in my iPhone storage?

How to check the storage on your iPhone, iPad, and iPod touch - https://support.apple.com/HT201656 - "If your device is low on storage, iOS automatically optimizes its available space while installing an app, updating iOS, downloading music, recording videos, and more. To make more storage available, iOS can remove some of your items, like streamed music and videos, files in iCloud Drive, and parts of apps that aren't needed. It also removes temporary files and clears the cache on your device. iOS only removes items that can be downloaded again or that aren't needed anymore."

Actually you can't really "move" them to iCloud in the sense of iCloud behaving as an external hard drive. iCloud is designed as syncing storage so anything in iCloud is also on any device you used with your Apple ID and signed into iCloud and using that service. As indicated in the article I link, you can use some iCloud optimization features to have it not fully sync everything with you device.

Throw things away or move them to iCloud.