Unfortunately, one of the compromises on a lot of mid-range and less expensive Android devices is a lack of internal storage. Manufacturers and carriers also add a lot of unnecessary apps (aka bloatware) that uses a significant portion of the already limited storage, and to make matters worse much of it can't be deleted unless you root your phone, which voids the warranty. I suspect this is contributing to the problem you are running into with lack of storage.
Other than deleting apps you don't use and going into you settings and clearing the cache for apps, there isn't too much you can do. If your phone supports an SD card you can move some apps to the SD card to gain some space, and you can save files such as photos to the SD card as well.
Some apps use a ton of space over time. If you use Google Music, pay particular attention to it because it will balloon in size. Go into your settings (settings>apps) and check the data and cache size to see if this is a space hog on your device, then clear the cache and delete data if you would rather have the space available to do things like download photos.