To add new languages to your profile, go to https://www.duolingo.com/courses, choose a language and select “start course.” You can change the language you want to learn from by using the drop-down menu on the top right of the page.
Adding languages will not make you lose progress in existing courses. You can switch between courses you’ve started by clicking on the flag icon in the top right corner of Duolingo and selecting a different flag from the drop down menu.
If you switch your base language (the language you are learning from), some of your existing language trees may "disappear" from your menu. Don't worry! They are still there. To visit them again, simply change your base language back to what it was originally. The skill trees displayed depend on what language you have selected as the base language.