Tzeentch embodies mortals' desires for evolution, improvement, innovation, and progress as well as their dreams of wealth, prosperity, hope and is the patron of schemers, scholars and sorcerers alike. He is the most perfidious of all Chaos Gods, he who weaves the threads that connect every action, plot and subtle intrigue in a galaxy-wide game of manipulation and subterfuge. At the end of each of these threads lays the ensnared soul of a human puppet; those of his servants and agents who believe they serve the Lord of Sorcery in mutually beneficial pacts. Everything related to the master of change shifts, mutates, evolves, and transmogrifies. One can go mad, and many have, trying to study even the smallest threads of the Great Schemer and to perform the impossible: to describe him and to fix him to one shape, one form, one motive, one truth. Perhaps the best way to characterise Tzeentch is not to describe him at all, as over time, he differs from himself more than he does any other being.
Tzeentch is the undisputed master of magic in the universe. Sorcery is one of the most potent agents of change, and those who use it are amongst the most ambitious and hungry for power. The use of psychic power, or magic as it can rightly be called, is held as the ultimate expression of faith among Tzeentch's followers, who have much to gain from his patronage. During a time, he used to the primary God over the Chaos pantheon, lording over all others through his Staff, which literally contained all of the Magic in the world. This was the one instance where it caused the other Gods to unite against him, which required him to shatter his staff as a peace offering. Tzeentch has since been trying to piece together the staff, whose shards dropped into the mortal world and each turned into a magic spell, by sending out the blue scribes to collect each and every shard by recording said spells. The reason he doesn't entrust this to a more efficient greater daemon is because anyone who possesses the staff would be stronger than even him, and the blue scribes are constantly at each other's throats.
Paradoxically, Tzeentch schemes for the sake of scheming - he has no end goal or objective, going as far as to derail his own plans and preventing Chaos from consuming all that exists, which one would assume was the whole purpose of it all along. The truth is that if Tzeentch ever allowed the Ruinous Powers to dominate, there would have been no more change to be made and his existence would come into a screeching halt. To prevent that from happening, he purposefuly sabotages his own schemes, weaving a bizarre web of ploys, turning wheels within wheels, gambits within gambits, each of his plans designed to sabotage another one of his plans which in turn sabotages another, and so on ad infinitum. Perhaps the most ironic of all (even more ironic than the atheistic Emperor of Mankind being worshiped as a living God) is that the God of Change enforces the status quo, keeping things as they are - insuring that the world is miserable and in suffering, but also preventing his own side from taking over to prevent their mutual erasure.
The mortal champions of Tzeentch are especially dangerous, as they often wield awesome sorcerous power on top of their considerable physical prowess. His most favored of all chesspieces are the Chaos Space Marines of Thousands Sons, one of founding legions of original Adeptus Astartes headed by Primarch Magnus the Red. He had specifically manipulated them to set into collision course against the Space Wolves after Magnus used forbidden sorcery to completely ruin a centuries-long project made by the Emperor. All because Magnus wanted to warn his father of Horus' treachery. The most treacherous of all, Tzeentch had manipulated these events to corrupt Magnus and rewarded him by elevating him to Daemon Prince status. As result of their worship of Tzeentch, the Thousand Sons suffer constantly with "gifts", mutating them completely out of control.