How do you cut your own bangs? Slowly. Carefully. Patiently. With low expectations and with tips from this site. I got lucky this time and I was able to turn my awkwardly grown-out side swept bangs into freshly cut straight across bangs. Make sure you cut them longer than you think you want them, hold your scissors diagonally cutting little bits at a time, taking breaks often to check your progress in the mirror and don't cut straight across!
Make sure you leave some longer bits at the side so the bangs taper off softly.