How will the Antichrist and the False Prophet be destroyed?
The Antichrist and the False Prophet will be destroyed by the spoken Word of the Lord Jesus Christ, who defeats them in battle and casts them alive into the lake of fire.
When the Lord Jesus returns, He comes as the rider on the white horse, clothed in a vesture dipped in blood, with a sharp sword coming out of His mouth. That sword is not a carnal weapon but His spoken Word, and Scripture shows that this alone is enough to win the battle. The armies of heaven follow Him on white horses, but it is His Word that smites the nations, for He will rule them with a rod of iron and tread the winepress of the fierceness and wrath of Almighty God.
The beast and the kings of the earth gather their armies to fight against Him, but the beast and the false prophet who worked miracles to deceive those who received the mark are taken and cast alive into a lake of fire burning with brimstone. The rest of their armies are slain by the sword that proceeds from His mouth, so that the fowls are filled with their flesh. Even though the Antichrist and the False Prophet once ruled the whole earth, they are given no dignity of burial; they are cast alive into the lake of fire.
The power of that Word is described through the prophets. Joel says the Lord shall roar out of Zion and utter His voice from Jerusalem, and the heavens and the earth shall shake. Zechariah describes a plague that comes at this Word: the flesh, eyes, and tongues of those who fought against Jerusalem consume away while they yet stand on their feet, and a great tumult from the Lord causes them to turn their hands against one another in confusion until the victory is complete.
The scale of this destruction is pictured in the image of the winepress: the angel gathers the vine of the earth and casts it into the great winepress of the wrath of God, and it is trodden until blood flows out even to the height of a horse's bridle for about two hundred miles. This shows that by the power of His spoken Word alone, the Lord Jesus utterly destroys the Antichrist's forces, establishing Himself as King over all the earth.
The scriptures
And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against him that sat on the horse, and against his army. And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone. And the remnant were slain with the sword of him that sat upon the horse, which sword proceeded out of his mouth: and all the fowls were filled with their flesh.
And the angel thrust in his sickle into the earth, and gathered the vine of the earth, and cast it into the great winepress of the wrath of God. And the winepress was trodden without the city, and blood came out of the winepress, even unto the horse bridles, by the space of a thousand and six hundred furlongs.
The LORD also shall roar out of Zion, and utter his voice from Jerusalem; and the heavens and the earth shall shake: but the LORD will be the hope of his people, and the strength of the children of Israel.
And this shall be the plague wherewith the LORD will smite all the people that have fought against Jerusalem; Their flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth. And it shall come to pass in that day, that a great tumult from the LORD shall be among them; and they shall lay hold every one on the hand of his neighbour, and his hand shall rise up against the hand of his neighbour.
For I will gather all nations against Jerusalem to battle; and the city shall be taken, and the houses rifled, and the women ravished; and half of the city shall go forth into captivity, and the residue of the people shall not be cut off from the city. Then shall the LORD go forth, and fight against those nations, as when he fought in the day of battle. And his feet shall stand in that day upon the mount of Olives, which is before Jerusalem on the east, and the mount of Olives shall cleave in the midst thereof toward the east and toward the west, and there shall be a very great valley; and half of the mountain shall remove toward the north, and half of it toward the south.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.