It is a pious Orthodox tradition to light candles for personal petitions and intercessions when entering the church and venerating the icons. Lighting a candle is making an offering to God. It is offering our prayers and thanks to Him for His blessings. We may light candles for ourselves, for the health of each member of the family and for friends. We also light candles for the souls of the departed. When we light a candle, we pray for the person for whom we lit it.
A simple prayer at the lighting of the candles would be to just pray the Jesus prayer for the person you are lighting the candle for: “Lord Jesus Christ, Son of God, have mercy on _____.” Another prayer, taken from a prayer priests say to bless candles, says, “O Lord Jesus Christ, the True Light, Who enlightens everyone born in this world, pour out Your blessings on ____, who we remember, and sanctify him/her by your Grace.” It is also fine to just pray from your heart.
Candles should be allowed to burn down without being extinguished early, since the burning candle symbolizes our prayers rising to heaven and the light of Christ in our midst. There are many other symbolic meanings to the lighting of candles. Lighting a candle is a symbol of prayer. It is also a reminder that Christ is the LIGHT of the world, and the FLAME is the Holy Spirit. When standing in church one is like the flame, alive and attentive to the Word of God. Therefore, it represents one’s presence in the church. Our praxis reinforces and teaches our faith, and the lighting of candles is a prime example.