How to crack walnuts?

At my house we use a butter knife. At the bottom of a walnut, there's always a small crack that we can slip the tip of the knife through, then twist the knife by the handle and the shells come apart. The little separator in the shell can also be easily removed with the butter knife.

But other than that, we sometimes opt to simply grab two walnuts, and with our two hands, crush the shells against each others, and one of the two walnut shells will Crack and give way. Disclaimer: this method can get messy.

In our family we use a screwdriver in the same way as the first answer uses a butter knife, (and I think that butter knife is more likely to be the safe choice.)
But for those nuts that resist and for most other nuts, we use a 'waterpomptang', which is translated to pipe wrench or tongue-and-groove pliers, you need the kind with the two legs and the adjustable jaws.
You need to set the jaws to the size of the nut, slightly smaller is the best. Adjust the power you put on the legs to the force the nut needs.

After the nutcracker type was added to the question…

Those are frankly the worst type of nutcracker. You have no control over how far the jaws close & not much leverage - so you tend to try get each nut as far into the jaws as you can to get enough force, then squeeze two-handed with all the force you can - risking nut, knuckles & any nearby glassware in the process;) Once the nut gives, the jaws slam shut, smashing the whole nut to smithereens.

Short of buying some expensive specialist cracker (that in most houses will get used once a year at xmas) then Willeke's idea of a pipe wrench is perfect. You have essentially an adjustable gap so you don't crush them & lots more leverage. You can get a really cheap & cheerful version for maybe $£€ 5 if you don't ever need to tug on pipe nuts, only walnuts.

If you're in the UK you need to search "water pump pliers" to get the correct type. Searching actually 'pipe wrench' or adjustable spanner/wrench won't find the right thing. A search on a 'proper' toolshop like B&Q, Screwfix etc will cost you 20 - 40 quid, but you can get cheapo on eBay for under £4. Perhaps also a supermarket or general tool stockist of the type you find at cheap indoor/outdoor markets (those stores that sell a 40-piece screwdriver set for 2.50 that will last until you need to actually undo a screw;) if there's anything like that open where you live & you need one for xmas day.

As these all have a click (or twist) adjust, you size it to close to slightly smaller than the nut, then fire away. Loads of leverage, loads of control & a measured gap that won't smash them.

Once you own one of these tools, you'll be amazed at how many other uses you can find for it - even if you never go anywhere near a pipe ;) Tight lids (be careful on glass jars of course), reluctant screw tops on anything, from food to glue tubes… Mine get far more use than the actual nut crackers buried at the back of the cutlery drawer.

I cracked a lot of walnuts when I was a child, as bowls of mixed, unshelled nuts including almonds, pecans, hazelnuts, Brazil nuts, and of course, walnuts, were our primary treats.

This is the technique for your nutcracker. I never had anything better, and I did it alot

Align the "split" in the walnut with the arms/jaws of the nutcracker. Apply just enough pressure to crack it into two halves. This will probably only crack one "end"...so rotate nut 180 degrees to work on other end. Once split (you may need to pry them apart with fingers or tool), take 1 half, rotate 90 degrees and crush very gently, enough to crack the half-shell but not crush the precious insides. With a good crack, you can remove a large part of the half-shell, if not the entire thing, as well as the internal inedible pieces that separate the walnut into four quarters.

With practice, you will not even have to split the nut before rotating 90 degrees to deliver the final crack whereupon you can remove big chunks of outer shell, leaving the internal nut ready to remove and eat by quarters (or halves if you also get good at removing that internal quartering support structure at the same time).