If you're speaking of "storage", then yes, you do need to be aware of the amount of free space you have available for your apps, etc. The size and makeup of your apps (and pictures, videos, app cache) do indeed consume storage.
If you're speaking of "memory" (i.e., RAM), you don't (and shouldn't) really do anything to manage that--let Android and it's Linux kernel manage those things for you (i.e., do NOT install an app killer or kill apps yourself).