For the pic you posted and assuming you are using Photoshop (process would be similar in other programs but might require different keystrokes.
1st option (easiest) -- Use the Magic Wand Tool and select the white circle that is one of the buttons - This will place a round circle around the outer edge of the button - then use Select - Modify - Expand to enlarge the circle half the amount you want your circle - (This will enlarge the selection circle so you do not cover the button white portion in the next step) (ie if wanting a 20 pixel border around the button expand 10 pixels) - Then use the same modifier except use Border (Select-Modify-Border) and enter 20 pixels (or how ever thick you wanted the circle) -- This will make a selection area that is 20 pixels wide with the center touching the original white button area - Use the fill bucket or paint brush tool to fill in the area with the desired color (repeat for the other buttons ( or Copy Paste that one and place around other buttons )
THis is probably the easiest method but the problem is PS is not the best at expanding and bordering circular areas so it may not create a perfect circle ( depending on the original shape of the button space )
2. A bit more involved but still fairly easy alternative -- If using a 300DPI image for the drawing ( best for good printing results ) and using normal buttons (1 1/8" diameter) - Use the Paintbrush tool and change the brush size to the dimensions of the outer edge of the circle you want ( ie. if wanting a 1 3/8" circle or 1/4" circle around the 1 1/8" button hole - set the brush size to 413 pixels (1 3/8" = 1.375" = 413 (300 pixels = 1 inch in a 300 DPI image ) - Place the brush where desired and left click to place a 1 1/4" circle in the desired color - Now change the brush to 338 pixels (1 1/8") and draw the inner button size circle in the center of the 1 3/8" circle in the color you want the button hole. ( just be carefull with placement to get it centered ) Now copy/paste that button hole with outline for the other button holes so that all are identical.
Hope I didn't confuse you too much !
Here's a quick jpg of the result using blue for the button hole with a 1/4" red outline around it !
EDIT : After rereading your post It seems you just want to draw the button hole circle -- In which case just use the paint brush tool with a 338 Pixel circular brush (1 1/8" if using 300DPI) - Place where you want the button hole and click -- You have a nice round circle the size of the button hole !