First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all people, for kings and all who are in high positions, that we may lead a peaceful and quiet life, godly and dignified in every way. This is good, and it is pleasing in the sight of God our Savior, who desires all people to be saved and to come to the knowledge of the truth. For there is one God, and there is one mediator between God and men, the man Christ Jesus, who gave himself as a ransom for all, which is the testimony given at the proper time. For this I was appointed a preacher and an apostle (I am telling the truth, I am not lying), a teacher of the Gentiles in faith and truth.

1 Timothy 2:1-7

Elections not go quite the way you had hoped? Pray.
Notice that Paul didn't prescribe a form of prayer to Timothy. What is important is not the way we pray, but that we pray. "Praying at all times in the Spirit, with all prayer and supplication" (Ephesians 6:18).
Are you concerned of the influx of liberal social ideals? Pray. Humbly beseech our Father to prevent them. Earnestly ask him to end embryonic stem cell research, to end homosexual marriage, and to end abortion. Pray against state-sanctioned atheism. Pray against the immorality and unethical behavior seen throughout the business world, media, and government.
Many of those elected, though belonging to a liberal party, have many conservative positions. Pray that they would stand strong on their conservative positions and not merely tow the party line. Pray for the Gospel to take root in our elected officials' hearts. What would happen if many of our elected officials humbled themselves before their Judge, repented of their sin, and turned to their Lord and Savior?
Pray for leaders throughout our nation and other nations. Intercede for others, especially our persecuted brothers and sisters.
Be thankful! God is still God of all the earth, and He reigns! Be thankful that America was established as a Christian nation and it can be such again. Be thankful for the majority of Americans, who still profess themselves to be Christians. Be thankful for our faithful brothers and sisters who are following the dominion mandate (Genesis 1:28) and are bringing the teachings of God into every aspect of our culture, and who are preaching the Gospel to every creature (Matthew 28:19).