The above should be read first. One can also browse some of the quotes on various articles on djinn that come up when using Google, such as Wikipedia's article (though these are subject to change).
I've heard scholars limit what can be physically attributed to them and say they can merely make suggestions, even visual suggestions, in the form of dreamlike thoughts (or hallucinations). That when they physically appear to us, it's due to their inserting of a hallucination in our mind and not their actual physical appearance. Allah knows best. Most Muslims are predisposed to the simple understanding that they can do either or.
I have also heard it likened to the effects of transcranial magnetic stimulation where a machine uses magnetic fields to induce weak electric currents which can alter the function of parts of the brain. The effects of this machine are known and documented.
How do the djinn do it? Pretty much the same way though without the need to use magnetic fields, they're beings of energy who can directly manipulate. The manifestation of this is, again, usually through thermal conduction, especially in the bloodstream. The Ma'ariful Qur'an commentary says,
He said, "Then give me respite until a day when all will be resurrected." He (Allah) said, "Respite is given to you." He said, "Then as You have made me go astray, I swear that I will sit for them (in ambush) on Your straight path. Then I will come upon them from in front of them and from behind them and from their right and from their left. And you will not find most of them grateful."(7:15-17)
What made Iblis speak the way he did before Allah?
The place where Iblis dared to speak was in the Most August conceivable Presence of the Master of all Honour where the awe and majesty of the occasion would not allow even angels and prophets and messengers to breathe. How did he do that? 'Ulama say that this was a sombre and highly cutting manifestation of the Divine wrath that, because of the rejection of Iblis, his view was so obstructed that he became blind to the grandeur and awe of Allah Ta'ala and irreverence came down to settle on him all over. (Abridged from Bayan al-Qur'an)
The Assault of Shaytan is Multi-Dimensional, not simply Four-Sided
In the present verse (17), Iblis is said to have identified four sides from which he planned to mislead the children of 'Adam, that is, the front, the rear and the right and the left. But, the purpose here is not to set up any limits. Instead, the sense is that this will be from all sides and directions. Therefore, the probability of his leading people astray from above and beneath the feet does not contradict it. Similarly, the saying of the Hadith that - Shaytan can enter the human body and move through the arteries and veins of blood and take command of the whole body - is also not contradictory to this.
The hadith in question says that Shaytan circulates in the human mind as blood circulates in it.
Other common manifestations of djinn "interference" (usually not the modus operandi of Shaytan though who is concerned with making people do evil, not disable them) include seizures which are defined as transient symptoms of "abnormal excessive or synchronous neuronal activity in the brain" (Wikipedia). In other words, disruption across a large portion of the brain of its neuronal activity.
What defense do humans have from djinn? Allah Himself it seems though we do not know if this is by means of some hidden mechanisms or His direct action. The former is not unreasonable considering the creation of Allah is usually ordered in some logical manner. All we can do is invoke Allah (the best way of which would be reciting the Qur'an and referring to scholars with experience in the matter who can advise on how best to mount this defense).
Determined djinn, according to Islamic tradition, can be very dangerous and hard to stop. They can simply circumvent a person's recitations or depictions of Qur'anic verses because they can approach, as mentioned, in a multidimensional manner. A person might put up a prayer or verses of the Qur'an on a door to "ward off" djinns, and it works most of the time. But if one becomes inordinately determined (not common, not in their nature to care so much) it can simply come straight through the cracks or under the door or over it or around the sides even while physically manifesting itself in some way. This is, however, extremely rare (in regards to numerous paranoid superstitions where people believe the slightest medical problem is being caused by djinn).
More often the djinn, especially the Shayateen, see the world as a one big non-stop party. Whatever activities humans are engaging in for pleasure, a djinn would want to "ride along" to feel the thrill. Sexual intercourse is an important example of such a situation. Allah has guarded the sexual relations of a husband and wife who invoke Him (not during the act obviously when in an impure state but before beginning). As for the rest of the people, djinns can seamlessly jump in and out usually without leaving a trace albeit likely affecting the mind in some subtle manner. In a divinely sanctioned union (marriage) between two people there is a synchronization of spiritual meaning behind the act and the biological mechanism (neurotransmitter and hormone release) which manifests as psychological/emotional connectedness. This process can become upset or skewed in any number of ways.