Always install/place applications and other data in external memory (memory card) if internal memory is too low, so that whenever any app runs it will get space to store temporary data in internal memory and because of this you can run multiple apps at the same time without any hassles.
Uninstall unnecessary apps when not in use for long time as it will eat up memory unnecessarily. You can install them again via setup files whenever you feel like through file manager or store them in computer or laptop and transfer them back when required.
Keep solely those themes which you are using currently and move/place rest of them in your computer. Doing this will not only free up memory but will also speed up your mobile.
Never run apps that doesn't seem to be supported by your phone like variation in screen resolutions, running apps which are compatible with higher Os.
Free up memory by deleting/moving songs, eBooks, videos, apps, wallpapers, images, old msgs, contacts and files which are not in use since long to computer. Import them back whenever required.
Never run heavy apps if mobile phone does not host enough RAM (Internal memory).
Shut down processes which are in the background when running heavy app. Mobile phone operating systems like android have inbuilt task manger through which you can close processes which are running in the background. You can download task manager like "Advanced task killer" or "Easy task killer" from application market.
Install smart antivirus software package on your mobile because if your device is infected with virus, it automatically slows down, virus can also cause fatal damage to the software. Delete unnecessary cookies, cache files.
If you're using a low budget mobile phone, make sure you do not run multiple apps at the same time.
While surfing internet do not run multiple tabs or perform multiple tasks because it slows down processor and consumes lot of RAM.
Free up internal as well as external memory as much as you can by deleting/moving unnecessary files.
Always keep your mobile phone software up-to-date