This is a very broad question, but i'll see if i can answer it in a general sense.
Cognitive thought is a global process, arising from a vast network of electrical and chemical signals coming together from many areas of different association areas of the cortex and deeper regions concerning memory, emotion, etc. Neurons communicate through a series of successive electrical signals passing from neuron to neuron, releasing chemical receptors to help determine the response of the next neuron in line (basically by changing the threshold needed for the receiving neuron to fire). Sensory information is processed and associated through specific pathways, put together in the cortical association areas, and stored through different mechanisms to form memories (another broad topic). The interplay between enormous numbers of neurons in specialized areas of the cortex forms the basis of thought and perception. Based on the information you receive from your senses and previous information stored in your memory about what time it is, how you feel, and what your plans are, etc, you can decide that it is time to get up.
Once the decision is made, the cortex will signal a deep area in the brain called the basal ganglia, which is responsible for initiating movement. These pathways in turn signal the necessary areas in the motor cortex that it is time for the necessary muscles to move. The motor cortex will send signals down the spinal column, which are fine tuned by areas in the cerebellum for proper coordination, to the appropriate muscles and cause them to contract or relax. Constant feedback from the sensory systems, your motor memory systems, and the cerebellum ensures that you are performing the correct series of movements and you physically get up.
This is a very basic description of what actually happens as a full explanation would be thousands of pages long, but if you're just learning the basics, i hope it helps.