1. Lock your fingers.
2. Put your palms on the lid. Bottom part, near the wrist.
3. Squeeze. You should hear soft air hiss.
You may do it without fingerlock but it helps, acts like lever. You don't need any tools for this method and lid stays reusable.
My preferred method is using a spoon to pry the cap. Once a bit of air enters the jar, it's stupid easy to open any jar unless it's so old that the contents are keeping the lid stuck (not your problem, i assume).
@T I prefer to whack/tap the lid with the blunt side of a knife in direction it's suppose to open all along the rim. This not only gets the lid to start loosening, but also provides little grooves for ease of grip.
No need to puncture the lid. Use a bottle opener to pry up the edge of the lid. This works with most lids. When I hit a lid that is too thick I revert back to using a screwdriver to pry the edge of the lid enough to break the vacuum seal.
Pickle jar lids are usually sealed under a vacuum, and that suction is why they hold on so tight. If you can puncture the top of the lid with a small steak knife, it will audibly sigh in defeat as it loses its suction and becomes open-able.