A simple request to God
Supplication is a word for earnest asking. In a prayer of supplication, you name what you need before God: wisdom for a decision, strength in grief, help with temptation, healing for someone ill, daily provision, or peace in a troubled relationship.
The Bible does not present God as distant from ordinary needs. Jesus taught his disciples to ask the Father for daily bread, forgiveness, and protection from evil (Matthew 6:11-13). Those are not vague spiritual ideas. They are real requests from people who know they need help.
Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God.
Prayer with thanksgiving
Paul wrote Philippians from prison, yet he told believers not to be consumed by anxiety. Instead, they could bring every concern to God through prayer, supplication, and thanksgiving (Philippians 4:6). Supplication is not pretending that life is easy. It is choosing to carry the need to God.
Thanksgiving changes the posture of the request. You can ask honestly while remembering God's past faithfulness, goodness, and care. That may sound as simple as, “God, I don't know what to do, but you have helped me before. Please give me wisdom today.” James specifically encourages those who lack wisdom to ask God for it (James 1:5).
For your needs and others' needs
You can make supplication for yourself, but it also includes pleading for others. Paul urged Timothy that supplications, prayers, intercessions, and giving of thanks be made for all people, including rulers and those in authority (1 Timothy 2:1-2). Intercession especially highlights praying on behalf of another person.
Jesus gave a striking example when he told Peter that he had prayed for Peter's faith not to fail during a coming trial (Luke 22:31-32). When you pray for a friend facing illness, a child who has wandered, or a community under strain, you are bringing their need before God with care.
I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men;
Ask boldly, surrender honestly
Supplication does not mean demanding that God do exactly what we want. Jesus himself prayed in deep anguish before the cross, expressing his desire while yielding to the Father's will (Matthew 26:39). That is a helpful pattern: be specific, be honest, and place the result in God's hands.
So a prayer of supplication can be plain and personal. Tell God what is happening. Ask for what you need. Thank him for hearing you. Then keep walking faithfully while you wait. Jesus encouraged his followers to ask, seek, and knock, trusting the Father's goodness (Matthew 7:7-11).
And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.