Shielding is a complicated subject, much more complicated than just a cursory examination will reveal. All shielding is based on a simple principle: no electric field can exist inside a closed, conducting surface. The Faraday Cage is the most basic example. A Van de Graaf electrostatic generator (used for the first atomic particle accelerator) depends on it. All shielding is frequency dependent, some more so than others. It is impossible, because of the energies involved, to shield against the penetration of cosmic rays. It is fairly easy to shield at very low frequencies approaching DC.
At my first real job, after my term of enlistment in the U.S. Air Force, was as an entry-level electronics technician at the University of Dayton Research Institute. When I was hired, the University was in the process of rapid expansion (which continues to this day!), having started construction on a new five-story engineering and research building. The Electronics Laboratory, where I was soon to work, was located on the top floor. We shared about one third of the available floor space with a materials engineering laboratory. Administrators and project managers occupied the remaining third with windowed offices surrounding the two laboratories. It was a pretty cozy arrangement, and I was destined to work there full-time while attending school part-time until a year after I graduated with a Bachelor of Electrical Engineering (BEE) degree, awarded by UD in 1978.
When we moved into the new building, one of the first things I noticed was a large "room" built inside one corner of the laboratory. It had walls with metal laminations on the outside and a large metal door with "finger contacts" that electrical sealed the door to the room when the door was closed. There was an air vent with a honey-comb metal structure inside that made it impossible to see directly through it because of internal reflections. I was told the vent stopped all radiation from DC to microwaves. There were also line filters that brought mains power into this shielded room, which I was told was a Faraday Cage.
I knew what a Faraday Cage was. We had one in our USAF Armament and Electronics maintenance shop, a simple wood construct with copper screening tacked to the wood and the seams soldered together. Nothing as fancy as the UDRI shielded room, but apparently "gud enuf" for guv'mint work. The UDRI Faraday Cage was intended for precision metrology work involving pico-volt and pico-ampere signals. Problem was, none of knew anything about metrology. So the Faraday Cage sat mostly idle while I was there. I think I used it for a project just once, and then only briefly because I soon discovered how to adequately shield my sensitive circuits.
Years later, at another employer, we had a contract to develop something for the Navy that required EMF (electromagnetic field) testing. Their requirements were very specific and we didn't have the facilities or instrumentation to perform the tests the Navy wanted to do. It took awhile, but eventually the Navy said "come on down" and use their facility. The Navy was mainly interested in microwave susceptibility over a very specific range of wave lengths (frequencies), but they also insisted on very precise measurements of the fields inside our equipment. This is where the rubber meets the road: we were trying to shield the inside of our equipment from the very thing we were trying to measure. The better we did our job, the harder it was to prove to the Navy that we had done our job. On the plus side, the Navy could crank up the output of their EMF generator until our probes inside the equipment could actually "see" something. We never did find out what the Navy really used their test stands for (they had several) but it made the UDRI Faraday Cage look like a tinker toy in comparison. Who would have thought that someone would want to put a high-power microwave transmitter and antenna inside a Faraday Cage?
You are on the right track in wanting to take measurements, but you need to temper that with the why and the how of it. There is a saying, possibly true, that "if it ain't broke, don't try to fix it." A good engineering design, which you learn how to do with practice, routinely employs good shielding principles, sometimes even when they aren't needed. Another saying, possibly true, "better to have it and not need it, than to need it and not have it." You can shield with adhesive copper tape. That's exactly what it's made for, among other uses. Whether it is necessary or not depends on your specific application.