How to manage storage without extra fees

Go to Settings > General > [Device] Storage. You might see a list of recommendations for optimizing your device's storage, followed by a list of installed apps and the amount of storage each one uses. Tap an app's name for more information about its storage. Cached data and temporary data might not be counted as usage.

How to check the storage on your iPhone and iPad

iCloud+ is a subscription service. You "rent" space in the cloud from Apple. But remember, space in iCloud is for backup - it will not be an alternative to your internal memory on your iPhone. If you lack space on your iPhone, then the only thing you can do is clean up so you get back the space you lack, or the expensive solution - buy an iPhone with more memory.

You can see what is taking up space on your iPhone here:

Settings → General → iPhone Storage

You can read about the difference between iCloud Storage and iPhone's internal storage here:

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