Question: I would like to know more about proper voice leading. I can hear each separate voice in a piece and I can hear chord progressions, but this seems like an either/or method for me. When transposing all voices, notes in chords are arranged in different orders and inversions. I would think about, for example IV-V-I, but I would not notice the bass line just simply moved down a whole step. How can I hear each note in each chord, and know exactly where it comes from and where it's going? When transposing it's naturally easier for me to transpose fingering (if such a phrase exists). I can transpose fingering to listen to it but I'm not sure if I have learned anything.
Albert's reply: Hearing every single voice in a multi-part texture is the most complicated of all ear training tasks. More often than not, it's overwhelmingly complicated, and fortunately we don't have to listen to all music this way. Except in special circumstances, it's generally overkill.
It's best to exercise the ear with chord progressions consisting of known chords. Don't worry about all the voices in the beginning: focus first on the bass, then the soprano (the lowest and highest voices). The bass is most important for harmony, the soprano for melody.
If you wish to go further, the next step is quite advanced. It's to learn the standard voice leading rules for 4-part harmony, something typically done only in professional music training. This involves writing 4-part harmony yourself. Part writing is definitely necessary for all professional musicians, but for hobby musicians it can be too much.
Once you're familiar with these rules, it becomes much easier to hear inner voices in music, since you know what to expect and can often infer what the voice leading must be because you know the rules.
One exercise I recommend is familiarizing yourself with standard chord progressions on the piano (I-V-I, I-IV-V-I, etc.). (I'll have to devise a worksheet with standard chord progressions for key-notes readers.) You'll get to know many of the rules intuitively this way.
Learn these essential chord progressions in all keys so that you're not only hearing them, you're playing them, and your ear training exercises as well as learning and playing new pieces will become much easier!
I wish to add that where it's really crucial to hear all the voices is in the pieces you play. It's generally not necessary (i.e., too complex) to try to hear each voice independently when you're listening to music, although it's good to listen to each instrument in an orchestra for instance. The brain can't concentrate on everything at once, so you just need to pick one or two instruments and listen closely to them.
In your pieces, sing (using the solfège syllables do, re, mi, etc.) each voice horizontally. That's the voice leading for that voice.
You can also simply play that voice on the piano by itself. Usually we tend to forget the inner voices... so this kind of practice is very helpful!
You also asked about transposition. If you simply use the same fingerings and try to play in a new key, you'll most likely confuse yourself and may well make mistakes. The key to transposition is to use the same scale degrees!