This is not an easy question to answer simply, and much is still not known.
The brain is a multi-layered ecosystem of hierarchically organized neurons, circuits, networks, and brain areas. The neurons emit pulses called "spikes" that last about 1 millisecond. Each neuron fires (emits a spike) on the order of 10 times per second.
These neural spike signals circulate throughout the brain in complex flows and interact with other signal patterns and channels through extensive multi-layered feedback loops and synchronized oscillating firing patterns.
Thinking is still poorly understood, but involves interactions between signaling pathways that are carrying information about the world and neurons that are representing information in "working" (short term) memory. The neural circuits representing working memory seem to do so via sustained firing until they are deactivated.
Decision-making appears to be a "winner take all" process in which many different neuron clusters representing alternate action choices compete by inhibiting each other. Evidence supporting each action choice increases the spiking activity of the neurons representing that choice. These neurons inhibit the neurons representing other choices, leading to a multi-way competition among neuron clusters. Eventually the evidence supporting one choice as optimal overtakes all the others and succeeds in suppressing the alternatives, becoming the clear winner.
Once one hypothesis or choice begins to overtake others, the activated neuron cluster (called a "cell assembly") sets into motion the processes of action and motor control that produces a behavior of some sort, such as announcing a decision or acting.
The above description is a dramatic simplification of what is actually occurring based on current theories and models. Almost none of this has been definitively determined yet.