It just takes a few steps.
Logged into the app now? Tap "More" on the bottom of your screen and look for "Account & Settings". At the bottom of the screen you'll find "Change Password".
Insert your old password and you'll then be allowed to insert your new password, which will be confirmed.
In case you've forgotten your old password, just log out. Then, enter your mySugr ID and when asked for your password, you'll see "FORGOT PASSWORD?". Click on that and faster than your diabetes monster can make a squeak, you'll have an e-mail with further instructions and a fresh, new password. But be careful - the code link to reset it is only valid for 30 minutes, so act fast!