When thinking about spatial understandings, it's probably best to start with geometry. (In fact, geography is essentially a very complex application of geometry.)
In geometry, you start with a point. Two points can define a line. Three points, and their connecting lines, can define a polygon. Two or more lines, joined end to end, can define (or at least suggest) a curve. Two perpendicular lines can define a plane. Each of the more complex understandings (polygons, curves, planes) builds off of the basics (points, lines).
In spatial understandings, there is a similar heirarchy of 'basic' vs. 'advanced' understandings. The basic understandings are sometimes called 'primitives' -- these are the simplest understandings of space that cannot be further reduced. The more advanced understandings are derived from associating across these primitives.
The most basic understandings of space are identity, location, magnitude, and time.
Identity makes each place 'knowable' -- it is its own thing. When we name a place, we are identifying some aspect of its identity. This is '15th Street'; that is 'Westside Park'.
Location is where this individual identity sits in space. If you have an absolute location system (such as latitude and longitude), each location can be defined on its own terms. If you have a relative location system (such as street addresses or 'north of the river'), each location will be defined by its position relative to other spatially-located objects.
Magnitude is tough to define, but basically it's the size of the identity and location. You might be describing a small space (a phone booth outside of City Hall), a medium thing (City Hall), a larger thing (the city), or an an even larger thing (the county, state, nation, and so on).
Time seems like an odd choice, given the fact that we're talking about space. However, our spatial understandings are bounded by time. Consider: What is your house like? Well, are we talking about the house you live in now or the house in which you grew up? If we're talking about your childhood house, are we talking about the way it is now or the way it was then? This time dependency is the same for everything else, on one scale or another: the United States in the 1950s has a different identity than the United States today (e.g., the pre-Civil Rights south); the United States in the 1850s even has a different location (and magnitude): Alaska had not been purchased, Puerto Rico and Guam were not territories, Hawaii had not been annexed, and so forth.
The derived spatial understandings are distance, angle & direction, sequence & order, and connection & linkage.
Distance is fairly simple: How far from one location to the next? You might wonder, "If it's so simple, why isn't it a primitive?" Because distance requires two primitives (two locations) to define it, it's derived and cannot be a primitive.
Angle & direction expands upon what can be done with two points: In addition to measuring the distance between, they can be used to establish a relative location. The latitude and longitude coordinate system, for example, uses angle and direction to set up what we use as absolute location: the east coast of the United States, for example, is about 40 degrees west of the Prime Meridian.
Sequence & order can be conceptualized as a subdivision of angle & direction: As you move along the west coast of the United States, for example, moving from San Diego to Seattle, you encounter other locations in a certain sequence & order (Los Angeles, San Francisco, and so on).
Connection & linkage creates sets of locations that 'belong together' -- they share common aspects of identity (Madison, Wisconsin and Lawrence, Kansas are both college towns) or they share proximate locations (San Francisco, Berkeley, and Oakland are all in the Bay Area) or they are found along a path (as you travel the Erie Canal from east to west, you pass through Utica, Syracuse, and Rochester).
Another set of advanced spatial understandings are spatial distributions, meaning that they exist in two-dimensional space. The earlier set of derived understandings could all be limited to linear (one dimensional) contexts, such as the cities along the Erie Canal. This next set of concepts all require planar surfaces to operate: boundary, density, dispersion, and pattern & shape.
Boundary is similar to region, from the old Five Themes of geography: many Americans recognize the concept of 'the Midwest' as a region of the United States; however, they may disagree as to where the boundary of the Midwest is: does it include the Great Plains states? Should the Great Lakes states be excluded? Or consider the concept of a neigborhood--where is the exact boundary? In some cases it may be quite clear (Harlem lies on the west side of the Harlem River, and the east bank is the Bronx) and in other cases it's uncertain (is Hamilton Heights part of Harlem, part of Washington Heights, or is it its own thing?).
Density is fairly simple: how much of something is located within a boundary? For example, Brewster County, Texas is a very large area (three times the size of Delaware) with a very low population; its population density is about 1 person per square kilometer. Quakertown, Pennsylvania was once singled out by the Guiness Book of World Records as having the greatest number of fast food restaurants within a square mile.
Dispersion is a refinement of density: within the boundary, are the occurrences evenly distributed or clustered? In Brewster County, the population is pretty much limited to Alpine, in the north end of the county. In Quakertown, the fast food restaurants are clustered on either side of Route 309, the main throughway.
Pattern & shape put together the concepts of boundary, density, and distribution and feed them into human creativity. A fairly straightforward pattern is the location of global population centers (e.g., Tokyo, Seoul, Shanghai, Delhi) along water sources: coastlines, rivers, and lakes. A more fanciful pattern is the association between the map of China and a chicken or the MIMAL figure in the map of the United States.
The Golledge chapter goes on to discuss higher-order spatial understandings (correlation, overlay, network, hierarchy), and these can again be understood as associations of the simpler concepts: location and connection combine to form network; location, magnitude, and connection combine to form hierarchy.
The main point to understand is that reading a map, any map, uses these higher order skills and (of course) the more basic concepts contained within them.
As discussed in the introduction, we are often unconscious of our use of these skills and take them in at a glance (seeing a shape or pattern on a map, or assigning a hierarchy among spatial concepts of continents, countries, and cities). As we use geospatial tools, however, we will be in a new space for each of these familiar concepts: Google Earth has certain labels to establish identity (e.g., the "Local Place Names" layer in Google Earth--it's in "Layers" under "More"); it has these tools to measure distance (the ruler). Furthermore, some tools have unique abilities to support and extend our spatial thinking: GPS units give us absolute location (which is a specialized form of angle & distance); GIS allows us to conduct rigorous analyses of density, dispersion, and correlation. To understand the tools, we need to understand the concepts they work upon. Because so much of our spatial thinking is unconscious, we need to be able to stop and describe it in its smallest component pieces: spatial thinking skills...taxonomized.