The card reads " When your turn begins, draw 2 cards and lose (click.)" Am I required to use this effect as long as wyldside is installed? And how can I uninstall it when I am ready to stop using the effect? (other than Aesop)

As long as it is installed, you have to draw two cards and lose a click. This is not optional.

Unlike programs there is no normal action (i.e. installing a program allows you to trash previously installed programs) that would allow you to trash it when you were done with it.

Asops is probably your best bet, sacrificial clone would also work but might be a bit much for getting rid of one resource. Other than those two nothing springs to mind that would allow you to get rid of it by choice.

Chopbot works too. Or getting tagged and letting the Corp it (rarely work).