Some claim that Jihad is coercing into Islam. What is Jihad? How should it be done?

Although, Arabic words, Jihad, Jidal, and Qital seem similar in their sound, there are clear differences in their meaning. While Qital means war and killing; Jidal means hegemonic struggle; Jihad has a wider meaning that embraces every kind of striving in Gods cause. Fisabilliah- striving in the way of God, clearly makes Jihad different than others; that is to say being in the way of Quran and Islam. Jidal and Qital in accordance with Gods commandment also involve strife, these came to be called Jihad as well.

A divine guidance from Quran to understand Jihad properly:
O you who believe! Shall I direct you to a bargain (a deal) that will save you from a painful punishment? That you believe in God and His Messenger, and strive hard in Gods cause with your wealth and persons. Doing so is what is to your own good, if you but knew it. (As-Saff Surah, 61:10, 11)

Namely, the aim of the Jihad is to bargain for the hereafter. Even if it has hard tasks and difficulties, it is nothing when compared with the torment of the Hell. Therefore, Jihad is not made to kill and send people to Hell, but to struggle (to defeat carnal selves) to be saved from Hell.

This type of Jihad is the name of a war of saving people from Hell.
The messenger of God received the commandment, Peaceful settlement is better (An-Nisa Surah, 4:128) and called people for striving in the way of God. He (pbuh) overcame the torments of those people who turned down this invitation and finally he was given permission to levy war against oppressors.

While granting a subsidy to the believers who fight in the cause of God is type of a Jihad, spending certain amount of fortune for the eternal bliss of humans in the peacetime is Jihad as well. Participating to a war in accordance with Gods commandment is Jihad, trying to do something for people to reach the dignity of having belief is Jihad too.

Wars without having sublime objectives, just for conquering lands and ruling over people for transient, worldly luxurious lives are not considered Jihad

What is the purpose of war? There are two: to defend ourselves against the enemy and to fight against the oppressors to open the gate of freedom and finding the way of God.

There is no compulsion in Religion. (Al-Baqarah Surah, 2:256) Nevertheless, it should be fight against those who tries to close the way of Paradise. If a group of people prevent some others from reaching the truth and true path of salvation, to fight against those is Jihad too. After having achieved that, individuals are let free to choose their religion. He rather accepts Islam or continuous to live his religion. If he chooses the second one, pays Jizyah ().

Hamdi Yazir of Elmali says that there are two different types of Wars. One is, The war of betterment and the second one is, The war of corruption. And, states that The war of betterment is the one that was ordained on believers.

Therefore, wars should be performed in a way of a prayer. And it should be attended even to the smallest details. These below given verses should be followed:
And fulfill Gods covenant when you have made the covenant (and any commitment that you made among yourselves in Gods Name), and do not break your oaths after having confirmed them; indeed you have made God your guarantor. Surely God knows all that you do. (An-Nahl Surah, 16:91) Fight in Gods cause (in order to exalt His Name) against those who fight against you, but do not exceed the bounds (set by God), for surely God loves not those who exceed the bounds. (Al-Baqarah Surah, 2:190)

Islam has drawn a clear line of distinction between the combatants and non-combatants of the enemy. As far as the non-combatant population is concerned such as women, children, the old, and the infirm, etc. And many other rules like the above given should be complied with.
The hadith, The true enemy of yours is your actual evil self clearly states our greater enemy.
The following wisdom waterfall that spilled from the holy mouth of the Messenger of God (pbuh), after the campaign of Tabuk is a great lesson for us: We are returning from the lesser Jihad to the greater.

The greater Jihad is a personal struggle against ones carnal (evil) self indeed. Our lives pass with this struggle. A moment long negligence would costs a lot. Material Jihad, on the other hand is not continuous. Believers are not responsible with this type of Jihad during peacetimes.

To be defeated by an enemy earns you a martyrdom or a Ghazi (warriors who fought for Islam) title. A personal struggle against carnal self is not like the previous one. It should be won no matter what. Defeat ends up in the Hell.

Satan is identified with nafs (mans lower appetites, evil self)
Surely, Satan is an enemy to you, so treat him as an enemy (do not follow him, and be alert against him). He calls his party (of followers) but that they may become companions of the Blaze. (Fatir Surah, 35:6)
O humankind! (Observe whatever God commands you. He has made you dwell on the earth, so) eat of what is on the earth provided it is lawful, pure and wholesome (in composition and religiously); and do not follow in the footsteps of Satan (who deceives both those who are followed and those who follow); indeed he is a manifest enemy to you. (Al-Baqarah Surah, 2:168)

That means greater Jihad is the one, which is done against carnal self and Satan. Wars against the enemies are lesser Jihads.