Question: "How is Satan god of this world (2 Corinthians 4:4)?"
Answer: The phrase “god of this world” (or “god of this age”) indicates that Satan is the major influence on the ideals, opinions, goals, hopes and views of the majority of people. His influence also encompasses the world’s philosophies, education, and commerce. The thoughts, ideas, speculations and false religions of the world are under his control and have sprung from his lies and deceptions.
Satan is also called the "prince of the power of the air" in Ephesians 2:2. He is the "ruler of this world" in John 12:31. These titles and many more signify Satan’s capabilities. To say, for example, that Satan is the "prince of the power of the air" is to signify that in some way he rules over the world and the people in it.
This is not to say that he rules the world completely; God is still sovereign. But it does mean that God, in His infinite wisdom, has allowed Satan to operate in this world within the boundaries God has set for him. When the Bible says Satan has power over the world, we must remember that God has given him domain over unbelievers only. Believers are no longer under the rule of Satan (Colossians 1:13). Unbelievers, on the other hand, are caught "in the snare of the devil" (2 Timothy 2:26), lie in the "power of the evil one" (1 John 5:19), and are in bondage to Satan (Ephesians 2:2).
So, when the Bible says that Satan is the "god of this world," it is not saying that he has ultimate authority. It is conveying the idea that Satan rules over the unbelieving world in a specific way. In 2 Corinthians 4:4, the unbeliever follows Satan's agenda: "The god of this world has blinded the minds of unbelievers, so that they cannot see the light of the gospel of the glory of Christ." Satan's scheme includes promoting false philosophies in the world—philosophies that blind the unbeliever to the truth of the Gospel. Satan’s philosophies are the fortresses in which people are imprisoned, and they must be set free by Christ.
An example of one such false philosophy is the belief that man can earn God's favor by a certain act or acts. In almost every false religion, meriting God’s favor or earning eternal life is a predominant theme. Earning salvation by works, however, is contrary to biblical revelation. Man cannot work to earn God's favor; eternal life is a free gift (see Ephesians 2:8-9). And that free gift is available through Jesus Christ and Him alone (John 3:16; 14:6). You may ask why mankind does not simply receive the free gift of salvation (John 1:12). The answer is that Satan—the god of this world—has tempted mankind to follow his pride instead. Satan sets the agenda, the unbelieving world follows, and mankind continues to be deceived. It is no wonder that Scripture calls Satan a liar (John 8:44).