One structure for prayer is given by the acronym "ACTS", representing adoration, confession, thanksgiving and supplication (or intercession.)  This is one order, where we start off focusing on who God is, and praising him for that. Others find a CATS pattern helpful, beginning by clearing out of the way the things that sadden God in our lives, before we can go onto praise him.  Let's look briefly at each in turn : 

Adoration is to adore God, to worship him and to fulfil the commandment to love him with all of our heart, mind and soul. As we spend time in adoration, we praise God for who He is - our Creator, our Sustainer and our Redeemer. (more about praise and adoration.)

Confession allows us to clear away the things in the relationship between you and God which are displeasing to Him.  All of us have sinned. St John writes in his epistle "If we claim to be without sin, we deceive ourselves and the truth is not in us. If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness." (I Jn 1:8,9)  (more about confession.)

Thanksgiving.  From childhood we are brought up to say "Thank You" when someone does something for us, or gives us a gift.  Each moment God is blessing us, every minute we can recall the wonderful things that God has done for us, and the gifts that we have been given. And so, we need to be constantly thanking God for his blessings. In writing to Timothy, Paul makes it clear that we also need to be giving thanks for everyday, worldly things " I urge, then, first of all, that requests, prayers, intercession and thanksgiving be made for everyone—  for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness." 1 Tim 2:1. (more about thanksgiving.)

Supplication or Intercession. Finally we come to ask God for our needs and the needs of others. There are many demands on our prayer time - many topics and issues that we could pray for, so we need to choose, and to be specific. (more about topics to pray for)

Pray for others.   In the epistles of St Paul, we read of him praying for those he has led to faith, and asking them also to pray for him. So, you too can pray for other Christians, and encourage them to pray for you. Pray for your familiy members, and for neighbours and friends. It's also good to pray for those who don't know Jesus to come to faith - many Christians have come to believe in Christ through the prayers of others.

Pray for world issues : for peace in difficult situations, for leaders and those in influential positions, for global issues such as care of God's environment, justice for the poor, relief of suffering in less developed countries, and other issues that come to you.

Pray for your own needs too. It's easy to neglect this, but Jesus encourages us to do so in the Lord's Prayer - the model for prayer that He gave us.