In everyone's daily exchanges with people there comes a time we will need to interrupt another person or persons to pass on information. For a polite and graceful submissive you should endeavor to not interrupt someone needlessly but to find an appropriate time to step into their presence. Often times I am sent as a messenger for my Dominant and have to politely interrupt someone to pass on the message.
A few good phrases to have on hand for this purpose are:
"I don't mean to intrude."
"May I have a moment of your time?"
"This one has a message from Sir Dom, may I proceed?"
"I humbly beg your pardon for my intrusion."
If you are wishing to speak to someone that is in a conversation with someone else, approach them but to not enter their sphere (the invisible bubble that people make around themselves) and wait patiently until you are acknowledged. You may go into a resting pose if you are trained in that, otherwise waiting with hands at your sides in an unassuming manner always looks best. Do not concern yourself with their conversation and it is rude to eavesdrop. Once acknowledged, then you may use one of the useful phrases above and pass on the information.
If you do interrupt someone unintentionally then apologize immediately and quickly so that they may continue with what they deem to be most important to them at the time. Of course, as you might imagine, not interrupting someone at all is the best and most polite thing to do.
As with this entire series, these are only my ideas and experiences and your own training and skill sets may be different. Feel free to customize any of the suggestions to fit your needs.