After the process of infestation, the Yeerk flattens itself into what has been described as "hammered-out Silly Putty" and sinks into all of the cracks and crevices of the brain. From there, all control is submitted involuntarily to the Yeerk. The host has no control over itself anymore.
And, since the Yeerk has access to all parts of the brain, it is able to pass flawlessly as its host (now called a Controller) so that nobody else suspects that there is, in fact, a secret invasion of their planet.
Known hosts: Gedd, Hork-Bajir, Taxxon, human, Andalite, Leeran, Garatron, horse