A visit to your Congressman, Senator or local/state representative is one of the more effective things you can do to affect how he will vote. You may visit either individually or, most effectively, as a group or representing an organization. Representatives will often meet citizens at their local state/district offices, so call and set up an appointment--you may be asked to put the request in writing and mail or fax it to them. A meeting allows you to have their full attention for your issue, unfiltered by their staff who may not share the same political views as the representative.
You can also visit their legislative staff--see Legislative Assistant (LA) above, particularly when visiting their Washington office. It can be much easier to visit or call directly city/county/town and state representatives.
Expect that a meeting with a Congressman, Senator, or staff member will be very brief, so make your most important points quickly and give him a packet of additional reading material along with your contact information; and ask him to contact you after he has reviewed the information to let you know how he will vote or take action. You may get a meeting with a staff member, and at the end, the Congressman might stop in just to say hello, giving you only moments to sum up your message to him; so be prepared with a 30 second summary (also known as an "elevator pitch" in other fields) for such opportunities.
In many cases, an elected official may not make up his mind how to vote on a bill until near the vote. Certainly top liberals and good conservatives will often know at the start how they will vote on clear-cut ideological issues, leaving a number of undecideds among the "moderates." Many bills are not so easily ideologically clear-cut, even if they offer "goodies" and pork to attract support from each side; and these bills may have greater numbers of undecideds. Thus your visit can get the representative thinking about the bill and your information might make the difference. The Patriot Act and the "stimulus" bills were extreme examples of how Congressmen often don't or can't read the bills before voting, and resulted in our freedom and economy being sold out. Their schedules are very busy and there are thousands of bills, so your visit may focus their attention on a bill or a part of a bill they were not aware of and never read. Always insist they read the entire bill, no matter how urgent is the perceived need, and no matter how many pages are in the bill.
You may chance to meet your elected representatives and their staff at town hall meetings, political fundraisers, meetings where they speak or get an award, local/state party meetings, parades and civic events; and you can take advantage of the opportunity to say a few words and give him your card or contact information. Don't expect to have more than a moment of his time as you shake his hand; but if your issue intrigues him, perhaps he will talk to you later or have his staff get in touch with you. Sign up at their websites for emails, as well as following their Facebook and Twitter feeds.
Left wing groups, student groups, unions, trade associations, and taxpayer-funded organizations are just some of the groups who regularly send large groups to each meet their representatives or staff; and when they hold annual or other meetings in Washington, they will devote part of a day for everyone to make visits to the Capitol, often carrying prepared briefing sheets, scripts, etc. Conservatives must match or exceed the numbers of liberal and special interest visitors to the Capitol. Such group visits are very organized but often effective; and you would be smart to emulate this successful action on your issue. Group visits make good media, so alert the press. Having everyone wear the same t-shirt, hat or button makes for great photos and video. The press may cover such group visits if you send out press releases and call/email reporters. You should also video your visits.
"It does not require a majority to prevail, but rather an irate, tireless minority keen to set brush fires in people's minds." Samuel Adams