a) "Prior art":
If you Google:
. . . skype piano lessons hardware
you'll get a bunch of hits -- some Web pages, and some YouTube videos -- that describe what you'll need. Of course, opinions will differ.
One thing nobody's mentioned yet is a decent Webcam. It doesn't have to be expensive, but it should be small enough to mount on a mic stand, and give your teacher a good view of your hands on the keyboard. That, and a bunch of other things, are covered here:http://www.theresemilanovic.com/taubman-tuition-info/info-on-piano-lessons-via-skype/http://musiclessonsresource.com/for-teachers-teaching-music-lessons-online-with-skype
b) One setup that is likely to work:
. . . Buy an audio mixer with a USB output -- e.g. Behringer Q802USB.
That is (essentially) a combined "audio mixer" + "audio-USB interface", in one box.
(I'm sure there are "How to use an Audio Mixer" videos on YouTube, probably with the Behringer 802-series for demonstration. It's a learned skill -- there are three different "gain controls", between the mic and the final output.)
. . . Buy a "dynamic vocal mic" (Shure SM58 is a professional choice, Behringer XM8500 is cheaper), or a good-quality "lapel mic"
. . . (check "podcasting equipment" reviews for those) with an XLR connector.
. . . Get a mic stand for the mic (if it's hand-held), and an XLR-to-XLR mic cable to connect to the mixer.
. . . Adjust the mic stand so that you can speak into the mic, from a few inches away, while you're sitting at the keyboard.
(No mic stand is needed, for a lavalier microphone).
. . . Buy (if you don't have one or two already) one (or a pair) of "multimedia loudspeakers" for your laptop. You won't need
. . . . "studio monitor" quality; something with 3" woofers and several watts per channel will be adequate.
. . . If your DP doesn't have "Line Out" jacks (separate from the 'Phone' jack), you'll be using the DP's "Phone" jack to
. . . get its audio output. You'll need a "stereo splitter cable" -- one end will fit your DP "Phone" jack, the other end splits
. . . into two 1/4" "TS" phone plugs.
. . . If your DP _does_ have "Line Out" jacks, you'll need two "guitar cables" (1/4" TS plug <--> 1/4" TS plug), one for each
. . . . "Line Out" jack.
. . . If the mixer requires software drivers, load them onto your laptop.
Wire the Skype inputs:
. . . Microphone --> "Mic Preamp" mixer input (it'll have an XLR jack).
. . . Left-channel DP output to a _line-level_ mixer input (1/4" phone jack)
. . . Right-channel DP output to a _line-level_ mixer input (1/4" phone jack).
Run a USB cable from the mixer to the laptop. Turn down the mixer gain controls. Power-up both boxes and the DP.
Start Skype, go to "Audio Settings". Under "Microphone Settings", you'll see several input choices. One of them will belong to the mixer (perhaps "USB Sound Device", but it could have another name). Pick that one.
Adjust the mixer controls so that when you speak into the mic, from a few inches away, Skype gets a good sound level.
Play on the DP, and adjust the mixer gain controls so that Skype gets a good sound level. If you're using "Line Out" from the DP,
you should hear your DP loudspeakers normally. If you're using the "phone" output, the DP speakers may be muted. In that case,
. . . Plug _open-back_ headphones into the mixer's "Phones" output (and adjust the mixer's "Phone Gain" for proper headphone volume).
That sets up Skype's "student-to-teacher" direction.
For the 'teacher-to-student' side:
. . . Plug the multimedia speakers into the laptop's "Phone" output.
. . . Adjust levels in Skype and on the multimedia speakers.
Make a Skype "test call" ("Echo" service). If everything is working right, you should be able to say a few words, and play a few notes, and hear them played back through the speakers without distortion.
The way this all works:
. . . Your teacher hears both your voice (through the mic) and your DP (through its "Phones" or "Line Out").
. . . You hear your teacher (he'll have a mic, and probably a piano), through the multimedia speakers.
_None of this is difficult_, the second time you do it. Expect some head-scratching, the first time.
Interfacing the Webcam is up to you -- but that's the easy part.
There are cheaper ways to skin the cat. But this setup is quite flexible, and should give you high-quality sound for your lessons.
PS -- written in haste. I _think_ it's all in place . . .