There are many inexpensive, or even free, Android phones being offered by carriers that may seem too good to turn down. Unfortunately, they may be too good to be true, though. Some of these phones are crippled with very limited internal storage space, and they may not even have an SD card slot for expansion. It's also important to remember that the actual usable space on the device will be less than what is advertised, because the operating system itself takes up space. If you already own a phone with little space and need to make it work, however, there are some things you can do to make it work.
One simple way to save space is to delete any apps that aren't being used regularly. You can also clear out browser temp files in Android's settings.
You can also offload photos and videos to Google Photos. This can be set up so that it will delete the photo from the phone once it's uploaded to the cloud. Then you'll be able to look at the thumbnails of the images on the phone, without actually having them stored there.
Another possible culprit for using up all available storage space is Google Play Services. One way that Google has been able to keep phones up to date without the cooperation of carriers is by separating some of the key ingredients of Android into apps that are actually on the Play Store. This Google Play Services component provides core functionality including authentication to Google Services, privacy settings, higher quality lower powered location based services. It also enhances your app experiences and speeds up offline searches, which requires caching more data on the device. If you go into Settings > Apps > App Info, you can manually clear that data and save space.