How do I change how I'm notified about new leads?

Go to Settings → Notifications. Every lead is always in your Leads inbox, whatever you choose there.

You can turn on Alerts on your phone for each device (with quiet hours), add up to 3 extra people to Lead emails (each confirms from an emailed link), turn on Lead alerts by text once your site is live (where texting is ready), and switch the Monthly report email on or off. On a free preview, lead emails are always on.

Each person sets their own phone alerts. Lead emails and texts for the whole team are set by the owner or an admin.