It shouldn’t be hard at all, and you won’t have to build anything. A couple hundred bucks of hardware and software should be plenty to get you started.
On your first questions about how much is beyond our range of hearing, the range most commonly given for human hearing is 20-20,000 Hz (cycles per second). This is for people 25 or younger. As we get older, high-frequency sensitivity falls off.
So outside that range is 0-20 and 20,000 to infinity, which if we took it literally would mean we can only hear an infinitesimal portion of the spectrum.
But practically speaking, sounds can’t have infinite frequency. There are limits that probably have to do with the mass of air molecules and stuff. (A real pysicist will probably stop by shortly to explain the upper limit of sound frequencies.)
In the animal kingdom, elephants and whales can hear (and vocalize) down below 1 Hz and mice can hear up to 100,000 Hz.
So if we take that as the upper limit for now, we could say that humans can hear roughly one-fifth of all frequencies, But this is misleading, since every doubling of frequency is an octave, making the human range about ten octaves. From 20,000 up to 100,000 is only another two and a quarter octaves. And from 1 to 20 Hz is four and a quarter octaves. So we can more properly say that humans can hear well over half of all sounds. (Of course, from 0 to 1Hz could be considered an infinite range, too, depending on how low you start, but let’s stay focused here.)
How to hear all this? Easy. Get a good microphone and a digital recorder–DAT, minidisc, whatever. Record whatever you want and transfer the file to your computer. Get a good sound editing program and process your files: to hear infrasonic sounds, apply a low pass filter to cut out sounds over, say 20 Hz, and speed up playback to move the sounds into the audible range.
It’s just the opposite with ultra HF files: High pass filter, slow the playback down.
You can get fancy if you want and try recording underwater. You’ll need a hydrophone, i.e. an underwater microphone, but then you can get some of those whale songs that were made famous in the 1970s. They were highly speeded up.
Of course, if you really want to get serious about that kind of thing, you could join the Navy and become a sonar operator. Remember “The Hunt for Red October?” They have some really expensive audio gear.
Good luck. Let us know if you find anything remarkable.