IANADoctorYet, but having recently finished anatomy perhaps I can offer some insight. I’m sure QtM will be around shortly to make me look like an idiot.
The construction and networking of nerves depends largely on their intended function. While it is not entirely accurate to say that one can trace a nerve from its origin (we’ll say a touch receptor on a fingertip) back to the brain, there is an unbroken chain leading from any innervated area into your central nervous system. When you poke your finger against a wall, the mechanical force involved pushes open a microscopic protein gate in the sensory neuron, starts flooding charged ions back and forth across the cell and starts a voltage fluctuation, an action potential, that propagates down the neuron involved. These action potentials are the “signals” that carry information to your brain.
However, nerves are not infinitely long. Your central nervous system (brain and spinal cord) is an isolated system. The voltage pulse carrying the “oh hey I just poked a wall” message from your fingertip will soon run out of room. Fortunately, that’s why we built synapses - connections between adjacent neurons that allow the signal to jump onto another “cable.” Synapses essentially turn the electrical activity into chemical messages - this is one of the first “processing” steps for nervous activity. Depending on the neuron and signal involved, the arrival of the action potential at the synapse might simply transmit the action potential uninterrupted and allow it to process down the neuron in question. Or, it might join other incoming signals to enhance or inhibit their messages, allowing for some primitive “networking.”
Inevitably, however, barring a few special exceptions, the signal will eventually end up in the spinal cord. On its way it might hop through a few more synapses or join other neurons into larger, aggregated structures (nerves), but the bundling of neurons in no way permits interactions between the two. When it reaches the spine, though, is when things get interesting. Different kinds of signals are routed in unique ways and isolated in discrete structures. In the simplest cases, the information might simply hop across another synapse and into the spinal cord for express delivery to the brain. Other kinds of information can be handled in complicated ways. Should the wall you just poked be extremely hot, not only will that “wall is hot” message shoot to your brain (through a different route and from a different neuron than “the wall is smooth”) but it might also loop straight around your spinal cord, close a reflex loop, and send out a signal to motor neurons in your arm to jerk back. Simple reflexes can bypass your brain entirely and occur before you’re even conscious of them happening. They’re “hard-wired” in if you will and short-circuit the typical top down control scheme of your brain. There are two rows of “ganglia,” collections of neuron cell bodies, that run parallel to your spinal column and several clustered throughout your body. These route and process information, usually unconsciously and frequently control vital organs.
Keep in mind that the spinal cord also contains specific pathways for certain signals, and that these pathways also lead into the lower, basic regions of the brain. Here, low-level, unconscious processing and signal filtering takes place. The message may inspire your cerebellum to make an instantaneous, minute postural change. You may be otherwise occupied and not notice it at all, for there is an extensive filtering system that decides which information is important enough to trouble your cognition.
Apologies if this is long and rambling and incoherent, as I’m still waiting for the excitation effects of my caffeine. 
The basic route might look something like this:
Sensory neuron -> Sensory nerve -> Processing into spinal cord -> Simple, quick action (if necessary), processed afferent signal ascends to brain -> Lower brain functions dictate reflexive action, or higher processes think and dictate proper action -> Processed efferent (outgoing) signal routed down the spine -> Motor nerve -> motor neuron -> activity