To extract the most lemon juice ‘with your hands’ can be interpreted a few ways.
If you’re looking for using no tools at all (other than a knife to cut it), then rolling it around on the counter to break some of the juice sacs before cutting and squeezing helps.
Some people also advocate for microwaving the lemon for a few seconds to extract more juice, but you may not want warm juice.
But if the question is how to do it without buying any new tools, there are plenty of things that you may already have that can help you extract more juice.
If you own tongs, you can use those as a crusher— just put the lemon half towards the hinged end, and squeeze at the working end.
Spoons and forks also work as a citrus reamer— insert them into the lemon half, squeeze the lemon around them, and then rotate the utensil to break up more juice sacs.
You can also use the back end of many wooden spatulas. (Beach or similar seem to work best; bamboo and smoother woods are okay, but don’t work as well)
If you’re considering getting a utensil for dealing with citrus, I would recommend a wooden citrus reamer. They’re usually only two or three dollars (US), and their rough surface does a much better job than a plastic or metal one.