The disciples believed in the existence of demons. They taught deliverance of them.

         Luke 9:1 Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases.

Jesus commanded His disciples to cast out demons.

       And when he had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease  Matthew 10:1.

               And so are we.   And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues;   Mark 16:17.

Jesus mentioned satan at least 15 times and taught the existence of demons.

          Jesus cast demons out of people, in Matthew 15:22-28 And behold, a woman of Canaan came from that region and cried out to Him, saying, “Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed.”
But He answered her not a word.
And His disciples came and urged Him, saying, “Send her away, for she cries out after us.”
But He answered and said, “I was not sent except to the lost sheep of the house of Israel.”
Then she came and worshiped Him, saying, “Lord, help me!”
But He answered and said, “It is not good to take the children’s bread and throw it to the little dogs.”
And she said, “Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”
Then Jesus answered and said to her, “O woman, great is your faith! Let it be to you as you desire.” And her daughter was healed from that very hour.

Satan's methods are expressed in Ephesians 6:11 as "wiles of the devil".

          His organization contains principalities, powers, world rulers of darkness and spiritual hosts of wickedness in high places.

                  It is in the lowest [of the 3] heavens above the earth that satan and his angels or demons live.

Satan and his organized empire of roving spirits are recorded in Ephesians 6:12 "For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places."

In God's Word, we find these demons/evil spirits living in human bodies. Fallen spirits are evil creatures. They are angry with God because they lost their place in heaven. Their main motive is to destroy what God loves. 

                          Since God loves the human race more than anything else, they wish to destroy them. When one becomes a believer, a constant warfare begins with satan.

Demons are personalities much like humans, but humans have a material body.

         Demons are personalities without material existence. They can't be seen with natural eyes. As fallen spirits, they desire to have earthly manifestations.

In satan's rebellion in heaven, he drew with him a great multitude of lesser angelic beings. Revelation 12:4 His tail drew a third of the stars of heaven and threw them to the earth. . .

         These are called  'the devil's angels'  Matthew 25:41 Then He will also say to those on the left hand, ‘Depart from Me, you cursed, into the everlasting fire prepared for the devil and his angels:

                  These unconfined wicked spirits are under satan's kingdom and dominion. They are his subjects and are so numerous as to make his power seem practically unlimited.

The word 'demons' isn't in the Bible, but their existence is evident. It does teach us that apart from satan, the prince and power of the air, there exist evil spirits of lesser degree of leadership and power.

        They are designated as demons by the Greek word diabolos, meaning adversary, false accuser, slanderer.

Paul told us to fight satan as with a person.

       Ephesians 6:10-12 "Finally, my brethren, be strong in the Lord and in the power of His might. Put on the whole armor of God, that you may be able to stand against the wiles of the devil. For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places."

Jesus did war against satan as a person.
         Luke 13:16 "So ought not this woman, being a daughter of Abraham, whom Satan has bound [think of it] for eighteen years, be loosed from this bond on the Sabbath?”

Jesus dealt with the devil/satan as a person.

        Matthew 4:8-10 Again, the devil took Him up on an exceedingly high mountain, and showed Him all the kingdoms of the world and their glory. And he said to Him, “All these things I will give You if You will fall down and worship me.”
Then Jesus said to him, “Away with you, Satan! For it is written, ‘You shall worship the Lord your God, and Him only you shall serve.’”

Satan's fall in Isaiah 14:12-15 "How you are fallen from heaven, O Lucifer, son of the morning! How you are cut down to the ground, You who weakened the nations!

       For you have said in your heart: ‘I will ascend into heaven,
I will exalt my throne above the stars of God; I will also sit on the mount of the congregation
On the farthest sides of the north;

            I will ascend above the heights of the clouds, I will be like the Most High.’

                  Yet you shall be brought down to Sheol, to the lowest depths of the Pit."

The personal names and titles given to satan.

        Revelation 20:2 " He laid hold of the dragon, that serpent of old, who is the Devil and Satan, and bound him for a thousand years;...."

Satan is not an influence or an idea or an abstract design. 

       He is a person. 1 Peter 5:8 '' Be sober, be vigilant; because your adversary the devil walks about like a roaring lion, seeking whom he may devour."

Jude 9 Yet Michael the archangel, in contending with the devil, when he disputed about the body of Moses, dared not bring against him a reviling accusation, but said, “The Lord rebuke you!”

         Michael, an archangel, a person of great power and position in heaven, refused to revile satan in a dispute over Moses body. Even in his fallen state, satan is still one of the greatest personalities ever created.

Satan's physical beauty and his many possessions, lifted his heart with pride. These have been his major tools in tempting people into sin ever since.

         If these things could produce iniquity in the " cherub that covereth" how easily will they produce iniquity in sinful flesh?

Satan's greed and lust for physical and material things replaced his spiritual service to God [Jehovah].

          Ezekiel 28:16  "By the abundance of your trading you became filled with violence within, and you sinned; therefore I cast you as a profane thing out of the mountain of God; and I destroyed you, O covering cherub, from the midst of the fiery stones."