For the f stops formula is this:

Large f-stop = Small opening

Small f-stop = Large opening

The larger number represents the lower end of the scale, less light entering the camera.
A smaller F-stop number means the opening is larger, more light entering the camera.
For a larger F-stop number requires a slower shutter speed.
A smaller opening means less light is reaching the camera, so it needs more time to create a picture or exposure.
A smaller F-stop number, requires a faster shutter speed. Less time is needed to create the exposure.

Slow shutter speed = larger F-stop number = less light being let in (smaller opening) = more in focus (larger depth of field).
Depth of field means the sharp area surrounding the point of focus.

General Mode Settings on cameras:

Fully Manual – ( M Mode )
Usually denoted by an M on the exposure mode dial. You select both the aperture and shutter speed yourself to obtain the exposure you are going after.

Aperture Priority – ( A Mode )
Usually denoted by an A or Av on the exposure mode dial. You select the aperture while the camera sets the shutter speed.

Shutter Priority – (S Mode )
Usually denoted by an S or Sv on the exposure mode dial. You select the shutter speed while the camera sets the aperture.

Common f stop ranges