Honestly, I'm gonna give you the sell-out answer.
The best way to determine what notes and chords are being played is with your own ear.
I'm sorry, but with all due respect to other responders, it's extremely difficult for any software program to detect chords, specifically. For basic triads, some of the best software can do the job, but so much of chord naming depends on context. And isolating a fundamental frequency is no cakewalk, either.
For example, for simple note naming, how would a computer know that a note with the frequency of 440 Hz is a B♭♭ in a C diminished 7th chord? The best computers currently can do is just give the most common enharmonic spellings for notes, but that creates tons of confusion. Never mind the fact that even single notes can be extremely difficult to pick out of a song, and they tend to blend with their harmonics. getting around that, though, at least is possible if you can just hook up your note-naming software directly to the interface of a keyboard.
Some other concerns bother me as well. How is a computer to determine where one chord stops and ends? When I play a C major triad, then play the note B, is that Cmaj7 or just a passing tone? Maybe it's even part of the G major chord that follows?
How can a computer handle the rootless voicings? Is that C♯ diminished 7th or A7♭9? Is E-F-A-B the basis of G13, or maybe an enharmonic respelling for D♭7♯9♭13, an altered chord?
The best way I can conceive of, until AI can just perform musical analysis faster than we can, is to learn a lot of music theory, build up your aural skills, and name them yourself, because no software on the market today can get the job done more accurately than a human.
There's a reason Music's SE is so successful. We need humans to answer most of the good questions on this site, because context determines so much of musical analysis.
Others have suggested slowing down the recording. That's a novel idea, and whenever I transcribe from audio I make use of any way I can to slow down the notes. I cannot understate how effective that is.