Regarding a kois shel brocho, a cup upon which one makes a special brocho such as kiddush, havdala, a bris, kiddushin, etc., the halacha is that one should rinse it on both the inside and outside before using it. You dont have to necessarily rinse it, you can wipe it from inside and outside; that could also do the job. If the cup is absolutely clean, it does not need to be rinsed although there are poskim who suggest that according to Kabbalah it should always be rinsed anyway. As mentioned, if one wishes to wipe it on both the inside and outside, that is also acceptable. Although al pi halacha a clean cup does not require rinsing or wiping, if one left it on the table throughout the meal and wishes to use it again for bencthing, it should be rinsed again before bentching.