How does the strips work? Do I have to have a driver for every strip. For example I build a table in my basement and I would like to have lights under the table and the shelve.
Not necessarily. But there are a few factors to consider. The two main ones are voltage drop and zones. If you want to control the shelves separate from under the desk then you will need a unique controller for each section. The voltage drop issue however will be completely dependent on what strips you get. High-density white LED strips tend to drop off in brightness after about 5 meters. Low-density ones can be run almost 10 without experiencing voltage drop.
If you want to use one controller and low-density strips then simply connect the end of one strip to the beginning of the next one with control wires. You should be good to go, but without knowing the specs of the strips, this isn't a guarantee.
I agree with @Gnant If you want color lighting get RGBW strips and a RGB controller that will work with HE. I haven't used the Shelly RGB controller on HE but I have used some of the other Shelly products and they are top notch and the custom HE drivers work well and the software app is very nicely done.
I am using an older RGBW device the H801 that isn't so polished as the Shelly but it works on Hubitat as well. However it does require you to flash the device with new firmware so you might look at the Shelly solution first.