Setting and Overview
There are a number of scriptures that seem to make a strong promise that God will give us whatever we ask Him for in prayer, as long as we ask in the right way. Of course, most people who are familiar with the Bible also know from the full teaching of Scripture and from personal experience that nowhere is such a promise actually given in the Bible, at least not in the way in which it is often understood. One could, and many have, compile all such promises, study each within its context, and from those strive to put together a comprehensive overview on what directions are given for prayer and what specific promises are given if we follow all of those. However, what is more valuable, is to understand each individual promise in its context. Although the promises that are given may be qualified, that does not mean that they are less powerful promises than may first take them to be, but rather more. Understanding the true promises, and what those promises teach us, should be our focus with Matthew 7:7-11 and the others.

Exposition
Verses 7-8 are organized around three verbs: ask, seek, and knock. These may or may not be intended to convey increasing intensity, but they are definitely intended to convey different emphases. Asking reflects an acknowledgment of need (Luke 18:1-14, Matthew 5:3-4.) Seeking reflects committing and taking action (Matthew 6:32-33, 13:45-46.) Knocking reflects boldness and access (Luke 13:23-27, Hebrews 4:14-16.) These do not necessarily mean that one must progress from asking to knocking, nor that one must do all three before God answers. Rather, the attitude that is behind doing one sincerely would also lead one to be willing to do the others (Luke 11:5-8.) That is why see all three receive favorable answers from God.
What are we asking/seeking/knocking for, however? In Luke, this exhortation comes after the Model Prayer, and when we reflect on the requests in that prayer, along with the attitude commended and exhorted through the Sermon on the Mount to this point, it seems to indicate that this is specifically referring to prayer for spiritual maturity, as equipped by the Holy Spirit (Luke 11:13.) Jesus has shown that He expects His followers to be obedient and have undivided loyalty to Him. Against such a standard we are all reminded of how unworthy we are. We can only aspire to such a standard if He equips us to do so.
His point is built further with an argument from lesser to greater. No human father would trick his child by giving them a harmful substitute instead of the thing they asked for and needed. Therefore, why would we think that God would? Absurdly, that is how many of us do approach God. We don’t ask because we don’t think that He cares enough to give us what we need, or He will punish us for asking in the wrong way, or He will instead give us what He thinks that we need (and we think that we know better.) James 4:1-3 lays bare such a mindset and leads us to self-examination for why we don’t ask, what we ask for when we do, and in what spirit we make our requests.

Examination and Application
If someone who was not familiar with God, but who believed you to be, were able to listen to your private prayer life, what do you think that they would conclude about God? If someone who was not familiar with you were able to listen to your private prayer life, what do you think that they would conclude about your priorities, and about the importance of your relationship to God? Our prayer life reveals a lot about us, and if we are spiritually mature, it should reveal a lot to others about God as well. We must examine our understanding of, and trust in, God’s gifts and will for us (Romans 8:28, 12:1-2.) We must also examine our relationship to God (James 4:8, John 15:7, Mark 11:20-24.) When those reveal room and need for growth, then we can reflect on and pray for revelation of God’s glory and holiness (Ephesians 1:17-19, 3:16-19.) As He reveals Himself more fully to us, then our prayer lives become more sincere, fervent, and effective.