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Go to the Apple App Store or to Google Play. I just updated my iPhone to the latest: 4.2.2. To find your version, in the Tesla app tap on your photo in the upper right...the app version is at the bottom.
@HWF 1st EV the above from @ronocoug is the correct answer. If you're using an iPhone, it's your only answer. If you're rocking an Android, you could sideload newer builds via apk mirror but for most users sticking to what's on the Play Store is definitely the right way to do it (even if you lag a few days getting the update after it was posted to apk mirror).