What kind of extensions are you looking at getting. If they are clip in hair extensions for instance, I would suggest removing them before dying your hair, as hair dye could strip the hair of its natural shine and leave it dry and course.
If they are more permanent like micro weft, sew in etc, then you could dye your hair whilst wearing the extensions, granted you purchase 100% human hair (preferably virgin hair, as its unprocessed hair).
However, if you can avoid dying the hair at all, I would suggest that you do this. Please see link to how to look after your hair extensions, which gives you all the do's and donts on how to maintain your hair. This article applies for all human hair extensions and I, (as a human hair extension user) have managed to make my extensions last for up to 6 months following this routine.