How should a believer endure persecution in the last days?
A believer endures last days persecution by developing the patience of the saints, refusing to worship the beast or take his mark, trusting the Father's will above self reliance, and embracing the fellowship of Christ's sufferings rather than being offended by them.
Scripture teaches that in the last days the church will face real affliction, hatred and even death for the name of Christ, and the way to endure it is through patience, the kind of patience that righteously bears trials without murmuring and holds fast to Jesus with joyful expectation. This patience is not natural; it is worked in us through tribulation itself, as Romans shows: tribulation worketh patience, and patience, experience, and experience, hope. The saints are told plainly that he who leads into captivity shall go into captivity, and he who kills with the sword must be killed with the sword; here is the patience and the faith of the saints. Even under the mark of the beast, endurance means keeping the commandments of God and the faith of Jesus rather than bowing to the antichrist's power.
Enduring persecution also means learning not to trust in ourselves but in God, as Paul and his companions did when they carried the sentence of death in themselves during their afflictions in Asia. They did not rely on their own judgment of the situation; they yielded fully to the Father's will, ready to be delivered or not, as it pleased Him. This same posture is required of believers facing the antichrist's power: our hope must rest on waiting on the Lord, not on escaping suffering, and we must not be ashamed of that hope even when it seems foolish to the world.
A vital part of enduring is recognizing that when the Body of Christ suffers, it is literally Christ Himself being persecuted, since He lives within us. This is illustrated by Jesus asking Saul on the road to Damascus, Saul, Saul, why persecutest thou me, showing that the persecution of the saints is persecution of Christ Himself. Understanding this changes suffering from something to resent into a fellowship with Christ, so that believers can say, as Paul did, that they bear in their body the marks of the Lord Jesus and are not troubled by it. Peter likewise instructs that if we suffer for righteousness sake we are happy, and should not be afraid or troubled, but rather sanctify the Lord God in our hearts and be ready to give an answer for our hope with meekness.
Finally, endurance requires embracing the mind of Christ, the same mind that was willing to suffer in the flesh, arming ourselves with it as a weapon against the enemy. Believers are called to rejoice as partakers of Christ's sufferings, to glorify God when reproached for His name, and to commit the keeping of their souls to Him in well doing, as unto a faithful Creator, trusting that after they have suffered a while, God will make them perfect, established, strengthened and settled in the faith.
The scriptures
And they worshipped the dragon which gave power unto the beast: and they worshipped the beast, saying, Who is like unto the beast? who is able to make war with him? And there was given unto him a mouth speaking great things and blasphemies; and power was given unto him to continue forty and two months. And he opened his mouth in blasphemy against God, to blaspheme his name, and his tabernacle, and them that dwell in heaven. And it was given unto him to make war with the saints, and to overcome them: and power was given him over all kindreds, and tongues, and nations. And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world. If any man have an ear, let him hear. He that leadeth into captivity shall go into captivity: he that killeth with the sword must be killed with the sword. Here is the patience and the faith of the saints.
And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name. Here is the patience of the saints: here are they that keep the commandments of God, and the faith of Jesus.
Because thou hast kept the word of my patience, I also will keep thee from the hour of temptation, which shall come upon all the world, to try them that dwell upon the earth. Behold, I come quickly: hold that fast which thou hast, that no man take thy crown.
And not only so, but we glory in tribulations also: knowing that tribulation worketh patience; And patience, experience; and experience, hope: And hope maketh not ashamed; because the love of God is shed abroad in our hearts by the Holy Ghost which is given unto us.
For even Christ pleased not himself; but, as it is written, The reproaches of them that reproached thee fell on me. For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope. Now the God of patience and consolation grant you to be likeminded one toward another according to Christ Jesus: That ye may with one mind and one mouth glorify God, even the Father of our Lord Jesus Christ.
And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me? And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks.
But thou hast fully known my doctrine, manner of life, purpose, faith, longsuffering, charity, patience, Persecutions, afflictions, which came unto me at Antioch, at Iconium, at Lystra; what persecutions I endured: but out of them all the Lord delivered me. Yea, and all that will live godly in Christ Jesus shall suffer persecution.
For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.