Youtuber Unit Lost knows how to lay out some very solid strategies and his explanation for how best to use Mercy is spot the hell on!
As he points out, the first place to start is in the controls section with some custom changes under Hero controls. You'll want to toggle beam connection to "on" so you no longer have to hold down the button to heal. Also make sure you turn the guardian angel prefers beam target to "off" so you can fly towards characters you aren't healing.
There's also a science and an instinct to knowing when to be healing and when to be giving out that 30% damage boost bonus. Check out the video for other important notes like when it's best to pop the ultimate and resurrect 1 or 2 important tanks or wait to bring back the entire team.