I hope and pray that millions of Christians will fast and pray for the upcoming election. My experience has been that many contemporary American Christians do not know much about fasting in conjunction with prayer. Here are a few insights, but it is neither exhaustive nor definitive.
1. Adding fasting to prayer is meant to intensify the prayer. Fasting is not a magical way to win God's favor. Rather, our emptiness and hunger for God is felt more deeply and focused in prayer.
2. We gain a sense of spiritual desperation and deep yearning by not eating. When we feel physical hunger, we should hunger and thirst for righteousness, as Jesus said. We should cry out to God with great earnestness and passion, as did David so often in the Psalms. Jesus himself called out to God, his Father, with great passion. See Hebrews 5:7-8.
3. We must be careful not to hurt ourselves physically through fasting. Some people cannot fast without endangering their health. Moreover, fasting may diminish energy, so you need to adjust your activities accordingly. Make sure to drink enough fluids. Dehydration is a serious problem. This is especially true in very dry areas, such as Colorado, where I live. You may also want to drink some fiber for digestive reasons. Going very long on just water can be physically hazardous. I rarely go more than half a day on just water. Consider getting some nourishment through fruit juice, vegetable juice, milk, etc. Know your physical limits. The body first starts living off of fat, then goes to muscle (which is not good). I can last a long time on fat; others cannot.
4. Try to spend extra time reading, meditating on, and praying through the Bible, especially those passages pertinent to your prayer/fasting focus. Isaiah 58 is apt for our present crisis, I believe. Of course, there are many other Scriptures to consume. Feed on the Word of God. We do not live by physical bread alone, but Jesus is the bread of life. Storm heaven through Scripture.
5. Jesus instructed us not to make a show of our fasting, as did the hypocrites. Secrecy is part of the discipline. However, that doesn't mean that no one can know. Those affected by the fast can be told without breaking the principle Jesus gave us in Matthew 6.
6. One can find encouragement by fasting along with friends. You can encourage one another in this endeavor of seeking God and perhaps meet for prayer during this time.
7. Posture matters in prayer. Pascal wrote that if we think posture alone is spiritually significant, we are mere externalists and thus deceived. But, if we think that posture means nothing, we are not taking our physical body seriously enough. Find the position that indicates reverence, submission, and desire for God's work in God's way, come what may! Getting on your knees or lying prostrate is advised.
8. Praying aloud may help your mind not to wonder and keep you from falling asleep.
Be countercultural for Christ: deny yourself, take up your cross and follow Christ--through prayer and fasting. Press into the abundant life he promised (John 10:10).