Somatosensory system anatomy
Firstly, some basic anatomy to help you decode Marks' ramblings!

Though it's hard to see the colours, the creamy kind of colour is the parietal
lobe. A fissure is a "valley" in the brain that separates the lobes
- in this case, the central fissure separates the frontal and parietal lobes.
A gyrus is the "hill", that is, the upper bits of the wormy looking
things (using proper scientific terminology as always!). So the postcentral
gyrus is the hill behind the central fissure. This area is known as the somatosensory
centre.
The thalamus is the big yellow blob in roughly the centre of the brain.

The thalamus is basically like a post office - it brings information in, sorts
it, and sends it off to the correct place. In this case, it brings in sensory
information collected by the spinal cord and sends it off to the somatosensory
centre in the parietal lobe.
Now, the spinal cord itself ...

Grey matter is where the cell bodies of the neurones are. White matter is
where the myelinated axons from the cell bodies come in and out of the spinal
cord. Some sensory information can come into the grey matter through the dorsal
horn (dorsal meaning "towards the back"), and then synapses with another
neurone cell body in the grey matter.
Within the white matter, there are areas which can be roughly grouped into
more specific areas - these are called columns, or funiculi (be aware that your
textbook may use this latter term). For example, the lateral columns run on
the outer left and right of the spinal cord, whereas the dorsal columns run
in the white matter between the dorsal roots.
Now, the diagrams Mark has given you:


Note that the thermoreception pathway is the same as the nociception pathway,
except for the first order neurone stimulation input (ie heat/cold or pain).
The main difference to remember (especially in a stressful exam situation!)
is that the low threshold mechanoreception pathway crosses sides (left-right
or right-left) in the medulla, whereas the thermo- and nociception pathway crosses
straight away in the spinal cord.