What you have to do is take a butterfly cork screw and use the extnding side as a wedge under the lid. That breaks the seal and makes it much easier to open the lid. As a substitute to the corkscrew, you could use a blunt knife or anything thin and rigid enough to put under the lid and pop the seal open.
If the top is too wide for my hand to grip it well enough, I tap the bottle top sideways onto the corner of a counter. That loosens the vacuum seal on the bottle and it will then open.
For a screw-top jar...
Run the lid but not the jar under the hot water - metal expands when heated and allows the jar to open easily. Then use a tea-towel to turn the lid.
I know this sounds weird, but when having this problem once, I used the rubber backing of my kitchen rug, worked like a charm, just don't spill the contents!
When I move into a new place, I use those rubber rolls to line my glass and dishes shelves. What I usually have left over makes for a good gripper to open any size jar.
As mentioned above, dish gloves. If that doesn't work and the container has been in the fridge, put the lidded part under hot tap water to let the lid expand and try again. If that still doesn't work, find a man (unfairly biologically superior in strength) to do it for you. He will do whatever it takes to open it, for his manhood will be at stake.
Use a bottle opener on the edge of the lid.
This "burps" the jar, if you will, and allows
some air to come out. If you don't have an
opener, try turning the jar over and smacking
the bottom of it.
if rubber gloves fail, carefully prise the lid underneath with the 'pointed' part of a bottle opener until the air escapes - this allows the lid to be unscrewed with minimal effort
If it's a small cap (like water bottles), I use a nutcracker. Otherwise, if it's a bigger one (like jam, tomato sauce...) I put the pint of a knife just under the cap and let some air enter. When you hear the tipical "click" then it should open
This always works for me.....Get a sharp knife and stab the top of the lid, letting air in thus making the jar a dream to open! (please be careful not to stab yourself)!