We've all done it. When our glasses are smudged up we reach for the corner of our shirt and clean them off. You probably even know that's the wrong way to clean glasses, but you do it anyway.
The reason your shirt is terrible for cleaning glasses is because it's likely filled with dust, and that scratches the lenses.
You also shouldn't use anything with ammonia, bleach, vinegar (although it's great for drinking glasses), or window cleaner because those chemicals strip away the coatings on your glasses.
Keeping your glasses in optimal shape is really easy when you do it right. That should be just enough to keep those fancy new computer glasses in optimal shape too.