Hi Amber!
Broken capillaries appear on our face because our skin thins out due to aging and sun damage. The amount of collagen and elastin in the dermis decreases and blood vessels expand, looking more obvious. They can be quite annoying if they get really obvious around the lower face (nose, cheeks, lips), and covering them with makeup is difficult.
At my practice we use IPL and long pulsed 1064nm/755nm wavelength laser to treat your problem. The intensity and wavelength selected would depend of the colour of your skin and the diameter of the capillary. It is normally quite pain free as we cool the skin rigorously after the treatment. There is also no associated downtime. A few (3-4) sessions would normally be required for complete clearance of all your visible capillaries.
Do get you skin looked at by a doctor who can give you further advice as there could be underlying skin conditions (e.g. rosacea) that would require treatment as well.
Hope this helps!
Dr Harvey Ho