To create a private circle on the web
Click the settings icon on the top-right corner of the left panel
Click Circles
Click the New Circle tab
Enable Make private button > Save

Note: To make private your existing circle: Go to Settings > Circles > Click the circle > Edit the details > Save
To create a private circle on mobile
Click the Circles icon in the lower-left corner
Click the Pencil icon in the upper-right corner
Click Start a new circle
Enable the Set as private button > Create
Note: To make private your existing circle: Click the Circles icon > Tap the circle that you want to set as private > Click the 3 dots on the upper-right corner > Click Edit circle > Enable the set as private button > Click update