Join a Republican Group that suits you. It is good to find and talk with other people that think as you.
Register and Vote! Nothing is better than doing your civic duty as a member of a representative republic.
Volunteer! Help out one of the many Republican organizations. Offer to help out in a polling place on election day.
Do you have a pet peeve? Something that excites or infuriates you? (like 2nd amendment, legislating from the Judicial bench, media bias, or frivolous lawsuits) Use that as a way to get started.
Do some research & get educated. There are some amazing resources out there to help you understand all manner of topics. Two of the oldest and most respected conservative organizations are The Heritage Foundation and the CATO Institute.
Write your Representatives. Telling your representatives in simple, clear statements is a great way to be heard. Add your voice to the chorus of others to help influence your Representative. Since the US isn't a direct democracy, you must elect those you think will best represent your views. Then you need to remind them what your views are! You should contact local, state, and national representatives. Don't forget the President!
Write editorials to newspapers. Having your opinion read by thousands of others does make a difference. It also has an impact on your Representatives. You will have to follow the rules set by each newspaper and be brief, clear, and concise. Come on, you can do it!