Even people who have some experience working with your issue will not have your expertise. Your message should be short and action-oriented. You should have concrete requests to present, but not more than two or three at a time. After you have established a relationship with an office, bring your international partners with you. They lend you a legitimacy that you do not have on your own.
Membership is a great lobbying strength.
If you are a membership organization, you should find out which districts your members are from and have them target their Senators and Representatives. If you are not a membership organization, you should think about forming a coalition so that your different partners can reach out to different Congressional offices. However, crafting a common message is difficult and you should not expect your coalition to last through more than one issue. An information sharing session is a good way to begin coalition building. Find Members or staffers who will act as champions for your issue and lend it legitimacy.