We come to another Psalm written by King David (second king of Israel and an ancestor of Jesus). This Psalm was written around 1,000 BC in the Hebrew language.
David cries unto the Lord to come to help him right now. Although God is everywhere, he needs God's help immediately. This is a good time to remember that the purpose of prayer is not to get our will done, but to get God's will done. Since we usually don't know God's will at any given moment in time, it is OK to ask for our will assuming that our requests do not violate any principal as taught in His world.
When we ask God to hear us, it is not that He can somehow ignore us and now He is paying attention when we are praying. It is about our realization that we can and are communicating with the God that knows all things and cares about our lives.
Therefore, this opening prayer request is not to make God aware of our situation. It is a prayer that God help us in the sense that we don't know what to do next and therefore, we are asking for His guidance in what to do next.
In verse 2 David says, Let my prayer be set forth before thee as incense; and the lifting up of my hands as the evening sacrifice.This is one of those verses where it helps to know the historical context to explain it. When God explained to the priests how He is to be worshipped, He explained that those priests were to offer animal sacrifices daily. The idea is to remind the priest that He desires to forgive our sins. He wants us to remain close to Him because we can come to Him "perfectly forgiven". Incense is what the priests offered up to God with their specific prayer requests. (See Numbers 28:1-8 on this principal.) The priests performed these rituals regularly, diligently and "did it like they meant it". What David wanted was his own prayer life to be as diligent and as regular as those rituals.
In similar fashion, we too should pray diligently and regularly. Does God notice us more if we pray this way? The benefit is not for God, but for us. If we are asking requests of God, it is up to Him to respond His way on His timing. The benefit of diligent and regular prayer is that it keeps our focus on Him.
As a child of God, we should want our life to be committed to serving Him. Because we care about Him, we do make the effort to seek Him this way.
Historically, think about those priests who made those ritual sacrifices. God gave them a job to do that was not impossible to do, but at the same time showed their commitment to serving Him. David still had time to do his kingly duties. The way I summarize it is we make time for God first, and then He provides the time to accomplish whatever else we need to do in our lives.