Don't go poking metal things into it!
I once ruined the arris (inside bevelled edge) of a lovely vase trying to clean the bottom of something.
I also nearly took my eyebrows off when I rinsed something with meths, then thought I'd burn it off! It did a very loud boom, and gave me a real fright!
I do the final rinse with distilled water (easily and cheaply bought as deionised water for irons and batteries),
then twist a taper of kitchen roll and stick it in down to the bottom - the tissue will absorb the water vapour.
The best thing I find - especially to start with, is that enzymatic clothes washing liquid, in a bit of room temp. water, give it a soak, then a swirl with copper balls.
To get rid of rust stains, minced raw onion shifts them.
Anything horribly smelly (perfume residue) can be made sweet again by rinsing with a dilute solution of sodium bicarbonate - but don't soak it - it's a bit alkaline, and glass doesn't like alkali.
Water stains need a professional person or at least professional equipment and stuff.
Try simple stuff before seriously nasty chemicals.