Once you're logged into the Facebook app, tap More in the bottom toolbar. Then scroll down and tap Settings.
From here you can change your General settings, which include your password. You can also monitor or change your Security settings, like your email login notifications. Tap the Lock icon to control your Privacy.
Other settings in this menu allow you to control things like your Timeline and Tagging, Videos, Blocking, Notifications, App settings, and even what Ads you see on Facebook. Just click the associated icon to adjust these settings accordingly.