How Do I Know What to Pray?

Sometimes I don't even know what to pray. How do I know what the will of God is in a given situation? I know from Jesus' words that I don't have to be afraid to ask. I can trust that He has my best interests at heart. God is wanting to give me good things in my life and my children's lives. I wouldn't give my child a dirty rock instead of a tasty, hot, baked roll and I am just a messed up human, so shouldn't I expect God wants to do good to me and mine?

 “Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. For everyone who asks receives, and he who seeks finds, and to him who knocks it will be opened. Or what man is there among you who, if his son asks for bread, will give him a stone? Or if he asks for a fish, will he give him a serpent? If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask Him!"  ~Matthew 7:7-11

The dilemma is WHAT do I ask God to do?
Sometimes I seem to contradict myself and worry myself sick that I could be praying THE WRONG THING. How then in confusing circumstances do I know what to pray?
Do I pray for someone who is terminally ill to be healed? Someone who is clearly hurting and ready to go to heaven, or that God would be glorified and many come to Him because of that godly person's death and clear witness? Do I pray for better circumstances for my child when I see they are clearly hurting or or straying, or that whatever it takes they would be where they should be? I have come to the point in my prayer struggles that I feel can be persistent in praying what I think is the will of God, and make my requests to Him, like the parable of the persistent widow in Luke 18, but I don't have to worry if I know His will perfectly, because.... 
He knows His own will! I can just pour my heart out to Him and He will work on changing me first. He can do exceedingly MORE than I ask! 

 
"Likewise the Spirit also helps in our weaknesses. For we do not know what we should pray for as we ought, but the Spirit Himself makes intercession for us with groanings which cannot be uttered.  Now He who searches the hearts knows what the mind of the Spirit is, because He makes intercession for the saints according to the will of God. And we know that all things work together for good to those who love God, to those who are the called according to His purpose." ~ Romans 8:26-28

At times I feel I should be like the woman in Jesus' parable that never stopped asking until she got her answer, at other times I feel I've pestered petitioned Him enough and I must keep giving the situation to Him every day if need be until it is resolved in His timing, and in His way. How many times have I looked back and said, "Thanks Lord, that You did NOT answer my prayer! Your way was so much better!" I can make my requests known to Him and rest, because He will guard my heart and mind and give me peace.

Then He spoke a parable to them, that men always ought to pray and not lose heart, saying: “There was in a certain city a judge who did not fear God nor regard man. Now there was a widow in that city; and she came to him, saying, ‘Get justice for me from my adversary.’ And he would not for a while; but afterward he said within himself, ‘Though I do not fear God nor regard man, yet because this widow troubles me I will avenge her, lest by her continual coming she weary me.’ Then the Lord said, “Hear what the unjust judge said. And shall God not avenge His own elect who cry out day and night to Him, though He bears long with them? I tell you that He will avenge them speedily. Nevertheless, when the Son of Man comes, will He really find faith on the earth?  ~Luke 18:1-8
  
"Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus." ~Philippians 4:6-7