File > Install Extension... and paste https://github.com/albertxing/brackets-tabs. Refresh Brackets (F5).
Download the ZIP. Extract into extensions folder. Refresh Brackets.
Show/hide sidebar View > Show/Hide Sidebar (Ctrl-Shift-H) toggles sidebar & tabs.
Switch tabs by clicking.
Reorder by dragging.
Feel free to submit a pull request if you find any bugs (to see a list of active issues, visit the Issues section). Please make sure all commits are properly documented.