I'm wondering how long after i have gotten my dental braces will i see a difference in straighter teeth?

Quite soon: I would say, "quite soon", as the exact number of months or weeks will be impossible to give without knowing your pre-braces condition and your idea of "straighter". With that being said, you will notice a nice change within 3-6 months in most cases. Ask your orthodontist/dentist how your teeth will be moved: if back teeth need to move a lot first, you may not see much difference for a while.

Immediately: By your first adjustment visit after braces are placed comparison of your pre-treatment records to your 1 month treatment status will show an improvement. Because it happens slowly, and you check movement daily, you don't notice progress. But comparison of status at 4-6 weeks after inception of treatment should reveal much change. Ask your orthodontic specialist to show you.