It's generally very difficult to measure the force very meaningfully, i.e. in some way that would let you compare different techniques, variations in timing/body-mechanics that you're aware of, even the same technique delivered by different people, or to predict the effect of the technique on different targets.
To understand why, it may help to consider what kind of measurement would be ideal, and I'd argue that's a set of (x,y,pressure,time) capturing (x,y) coordinates on the target or striking tool, and the instantaneous pressure (e.g. kg/cm2 or psi) at each point in time. For surfaces like the fist or fingertips hitting something that doesn't deform much, you'd want samples every couple millimetres, whereas for larger flatter less bony surfaces like the instep hitting softer targets like a punching bag, there's unlikely to be huge variation in pressure within a couple cms. I'm not sure how many times per second you'd need to capture to make sure you didn't miss peak pressures when hard surfaces collide, but I'd guess it'd be order-of one to two thousand hertz (i.e. pressure measurements at each point across the surface per second). It might help to imagine a "heat map" - much as the weather forecast on TV might show a map with blue/green/yellow/orange/red contours representing air pressure as a storm builds and fades over time, your striking tool and the target will form a map of waxing and waning pressures during the strike. For example - an animated gif such as this could encode how the pressure builds at different points during a strike (but you'd want a lot more samples).
What's more important - localised peak pressures that may shatter the point of contact, or sustaining lower pressures for longer times over larger areas that will bend the target to its breaking point - differs with the target material and structure. The contrast is similar to the difference between striking with a (pointy) pick, a blade, or striking with a sledgehammer or wooden mallet: the area, shape and hardness of the contacting surfaces affect the instantaneous pressures.
Now, getting gear to take such pressure measurements across a surface - I'm not aware of any commercial offerings in this space that someone could afford for home use. Closest I've come across is a 700Hz 200PSI 16x16 grid at about US$15k. 200PSI isn't nearly enough for a powerful karate punch with the top of the knuckles. If I find anything later I'll update this answer....
Even with ideal gear, it's important to understand that the measurements won't just be a function of the strike - how much the target yields during the strike is also a major factor. Specifically, a harder and heavier target will register higher instantaneous pressures (both in time and space) than a softer, lighter target that shapes itself around the striking tool (e.g. fist, foot) more, and is easily accelerated to the same speed as the striking tool (which is when pressure becomes 0, as there's no net force imparting further acceleration on the target).
These TV shows that have claimed to quantify different arts' strikes with a single "PSI" reading are tacky entertainment and shouldn't be mistaken for scientific. For example, a boxer wearing a glove is going to be making contact with at least 25cm2 striking area, so you only have to hit with 1/50th of the effort if you rap the target with the bottom edge of one knuckle - an area of about half a square cm - to register the same PSI reading, if the equipment's accurately giving a peak PSI reading.
Note the above also assumes the sensor can be trusted. A problem for cheaper sensors and home-made measurement attempts is that more intense strikes - with greater impact in a lesser time - may transfer energy less efficiently. For example, more energy may be lost to sound, localised deformations/stretching of the materials at the immediate point of initial contact. Similarly, with less time for pressurised air to escape from the target, the air pressure may resist the strike and distribute the impact over a larger part of target - energy expended in stretching the materials, again making the peak pressure and especially peak pressure per unit area "visible" to the sensor less. Some sensors may attempt to correct for this, but given a wide variety in striking surfaces and pressures it's an unrealistic ask for reasonably priced gear, particularly for small striking surfaces like the knuckles.
As an extreme example of how a seemingly simple and legitimate way of measuring impact can be flawed, consider the idea of seeing how much a kickboxing heavy bag swings when punched: a really good punch may fold the bag around the fist, such that the bottom and top are jerked towards the fist and the front surface material of the bag snaps taught and stretches against the further penetration of the fist; with the top of the bag naturally imparted a tendency to fold down but actually held up by a chain, straps or rope, the roof or frame holding the bag will undergo a sharp tug downwards and the bag upwards. All these forces and movements tend to be perpendicular to or against the direction of the punch, and they make it harder for the punches impact to efficiently convey momentum to the rest of the bag, compared to a slower "pushing" impact over a larger surface area.
In this case, you'd get a considerably better indication of punching power from a shorter, fatter bag that has less tendency to fold, especially if there's some stiffer material running vertically through the bag to help convey impact at the middle to the top and bottom, but any impression you get of power will still be very vague. You also trend towards more meaningful measurements/impressions of overall power for techniques that impact over a longer time and with a larger surface area: for example - a front kick with the flat/sole of the foot into a heavy bag will convey a better sense of the intensity of impact through the bag to a holder than a tai-chi style slapping palm, delivered with the hand slapping down from above the shoulder, which generates a very sudden short-lived shock of power with little follow through.
What's wrong with an accelerometre or high speed camera? Well, they don't tell you much about the body weight transfer and muscular tensions behind the strike, potentially encouraging flicky technique that wouldn't actually do useful damage. Some other devices will register better "scores" for slower thudding impacts, discouraging the speed and snap needed to break lighter, unsupported or retreating targets. And it's very unlikely that a device will encourage good habits across a variety of strikes.
So, my advice is just to get a heavy bag and a "big mitt" like they use in kyokushin karate and try to hit through them as hard as you can. Use your art's body mechanics, common sense, any science/physics you know and a good deal of experimentation and partner/instructor feedback. When you're ready, break some things. Let that take you as far as it will, without worrying too much about "scientific" measurements when most things out there marketed as such or readily DIY-able are of dubious accuracy and value.