To bring up the emoji keyboard menu on a Mac, press Command+Ctrl+Spacebar.
With Windows 10 or later, press WIN + “.” (the period punctuation mark), or else the WIN + “;” (semi-colon). Either will open the emoji keyboard.
For skin tone selection on a Mac, press and hold the pointer over an emoji. If skin tones are available a window will pop up. On Windows 10 or later, in the top-right of the emoji menu is a small box showing the "people" emoji menu. You can select skin tone from there.