Put your laptop on mains power. You need as much power as you can when you work with audio and video.
There are two ways to use Zoom: in the browser (i.e. type in zoom.us and join a meeting), or by using the Zoom software that you've downloaded to your machine. Using Zoom via the browser is fine for basic usage, but doesn't include all the features: for example, only meetings and webinars on the Zoom desktop software support stereo audio. And another gotcha: recordings and the Zoom mobile app don't support stereo audio.
Disable 'automatically adjust microphone volume' - if you don't, loud instrument sounds like trumpets can reduce the audio to low levels. Enable Original sound in Settings, which ensures the highest possible quality.
UPDATE Sept 2020: Zoom have added a "music mode" to the settings to accommodate musicians needing the best sound. For details on how to set this up see the excellent blog from MusicRepo.
Use the best microphone you can afford. Good quality headset mics start at £25. Lapel (lavalier) mics are used by most TV broadcasters for interviews because they pick up less background noise. Wireless versions are expensive but wired lapel mics start at around £60.
Be careful of using HD video in Zoom - enabling this could seriously slow down your call!