To the person who is under severe attack by the devil and who does not understand the character of God, Satan can seem extremely powerful.  At times, a person may even be tempted to believe the lie that the devil is God's equal in power, but nothing could be further from the truth!
Satan is a created being and, like all of God's creatures, is subject to the final authority of God.  Satan is not permitted to do anything unless God first allows him.  In Job 1 and 2, God granted permission for the devil to touch Job's possessions and even his physical body, but refused to allow Satan to kill him.  And, shortly before He went to the cross, Jesus warns Peter that "Satan has demanded permission to sift [him] like wheat" (Luke 22:31) and tells Peter that He is praying that his faith will be strong.  Clearly, Satan is bound by the authoritative decrees of Almighty God.  The devil has to ask God for permission before acting; he does not have equal authority with God.
Neither does Satan have God's great wisdom.  God's understanding is infinite (see Psalm 147:5) whereas Satan's is limited.  The devil, for instance, obviously did not understand that the death of Christ on the cross would soon be followed by His triumphant resurrection, His ascension to glory and the giving of the Holy Spirit to empower all believers.  If he had known all that, he would never had conspired to put Him to death (see 1 Corinthians 2:8)!  Furthermore, the Bible teaches that "nothing in all creation is hidden from God's sight" (Hebrews 4:13, NIV).  Only God "knows the secrets of the heart" (Psalm 44:21, NIV), and Satan is unable to perfectly read our minds.
As you begin to better understand who God really is and who you are in Christ, you will see that you have no need to fear Satan's power.  He is a defeated foe, and in Christ you have all the authority you need to discern his schemes and resist him (see Colossians 2:8-15; James 4:7).