For instance several artists like Andy McKee or Don Ross use capos on the majority of their songs. When trying to learn their songs by ear how would you determine where to put the capo and what tuning to put the guitar in?
The other answers address the issue of choosing a capo position to fit the chords you want to play. When trying to match a recording, you also use clues from the sound of the recording.
To determine the tuning, pay attention to any drones in the song. With an alternate tuning, the goal of the original choice of tuning is often to select these drones.
Determining the capo position can rely on the overall tone of the guitar and the chord voicings. Particularly the G and C chord shapes in standard tuning are more difficult to play as barre chords. So if you can pick out when those two voicings are used, it strongly indicates where the capo is.
Expanding on Lee's good answer- taking a 3 chord song. To play with open chords, the options are 1. E,A,B7. 2.D,G,A. 3.G,C,D, 4.C,F,G. 5.A,D,E. Let's take a song that's played in concert Bb. To use option 1, capo at fret 6. For option 2, capo at fret 8. Option 3, capo at fret 3. For option 4, capo at fret 10, and option 5, capo at fret 1. Not all options will be practical on all guitars, but nevertheless will all allow the piece to be played, in key, using open chords and capo.The sound of the 'open' strings is different from barred notes, and this is a good reason why sometimes a capo is preferred.
When other chords come into play, such as the relative minor, opt. 1 will use C#m (hardly an option!), 2 uses Bm; 3 uses Em; 4 uses Am and 5 will have F#m. Other related chords may or may not be a good choice.
The voicings of the various options will be a deciding factor in some numbers- the 2nd (D) and 4th (C) sounding sweeter than the others, due to a major third on the top of each chord.
EDIT : to answer the question, per se - identify the top note of a chord, the I chord preferrably. This will usually be the 1st, 3rd or 5th of that chord/scale. If it's the 1st (root) then option 1 or 3 will give capo placement. If it's a 3rd, then option 2 or 4, and if it's a 5th, the only option is 5.
What tuning is a thorny matter. It's very difficult to check that. I had to transcribe a song for a pupil last year, and the only clue to the tuning was a badly played guitar, where the strummer happened to strum a completely open chord - couldn't change quick enough. That showed what the guitar was tuned to. It's not always as easy as that, though.
This depends entirely on what you are aiming for. Personally I don't mind having to play one or two barré chords per sequence, while others will have completely different feelings about it.
An example is the E-key: If I have a chord sequence such as
E-B-C#m-A, I often place the capo on the fourth fret, so that I can play it as
C-G-Am-F instead. On the other hand, you could place the capo on the second fret, playing the chord sequence as
D-A-Bm-G. There is almost no difference in difficulty between these sequences, so the choice will depend entirely on what you enjoy playing.
I simply suggest you try to find out your own preferences by trying everything out. When I personally start playing a chord, usually it only takes me 3 seconds to figure out where I'll place the capo, simply because I've played each key in various settings so often before. As this is something that so heavily depends on individual preferences, I'm afraid that this is the only way to go about it.