How can I alter a square image into a circular one in Sketch?

That’s actually quite easy. There are two ways to do it:

1. Use a Mask

Best way IMHO, as it gives you more flexibility / editing options.

1. Import your image:

   

2. Draw a circle that will mask your image:

   

3. Move the circle behind the bitmap using the Backward toolbar icon:

   

4. Use the circle to mask the bitmap, by selecting it and choosing Layer › Use as Mask from the menu:

   

5. Ta-da!

   

6. As an extra step, you can group your bitmap and the circle mask, to stop the circle from masking other shapes:

   

7. To add a border: add another circle shape placed above the masked image.

2. Use a pattern fill

1. Draw the circle where you want your image to appear:

   

2. Select Fill › Pattern Fill in the inspector:

   

3. Click Choose Image… and select your bitmap:

   

4. Set the fill options to Fill in the drop down:

   

5. Add a border to the circle as you normally would.

6. Ta-da!

Hope it helps!