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When navigating in the backcountry, you'll usually bring a topographic map that shows the terrain so you can tell if there will be steep slopes or cliffs that might make the route difficult.
A sample topographic map is:
How do I read and understand the map? What do the lines and numbers mean?
A topographic map, as we see here, is made up of a number of lines.:
Every point on a given line is at the same elevation.
Where the lines get closer the slope is steeper, and vice versa. But that doesn't tell you directly which way the slope is going, so they put numbers on the lines - the slope goes up towards the higher numbers.
These numbers indicate the line's actual altitude, this can be height above sea level or above a particular reference altitude, usually the lowest or average point in the area.
The map's legend should tell you what the reference and units are, from the numbers here I'd guess it's feet above sea level (a mile up, so perhaps somewhere in Colorado).
The map shown in the question indicates what a number of features look like. Hills and holes are concentric circles (look at the numbers to figure out which), and when you have lines getting very close or joining (even going under another, see the upper-left corner), that's a cliff.
The path of steepest ascent (or descent) is directly perpendicular to the contour lines; the black lines seem to mostly be following one such path, especially the dashed branches. So if you like a challenge, walk across the lines, if you prefer to stay flat, walk along the lines, and for a gradual ascent, walk somewhere in-between.
I am only familiar with US topos, but a point the other answers miss is that the US Geological Survey have mapping standards, and most non-USGS maps (at least in America) match the USGS standards.
I'd suggest you start by learning the standard symbols in your area. Make up flash cards and you can easily quiz yourself as you have a few minutes (this is a great way to pass time while on the bus/train to work).
As for being able to navigate, topos often have more information than is necessary to walk through the woods and come out alive. For example, there are 3 symbols for a mountain top. The only difference is the precision of the measured altitude. There are 2 symbols for mines (vertical/horizontal). The brown elevation lines mark hills and valleys one way, but a depression another way (a circular pattern with lines pointing to the bottom of the depression).
I was taught orienteering by a few folks, and the fancy ways didn't really work for me, but finally I met an old, grizzled marine and his method was dirt simple, and works for me:
*Yes, sometimes this does not work out because the tree the next blaze is on has fallen due to weather/disease/forest thinning, etc. But works 95+ percent of the time.
With these maps it's all about elevation - just remember a few main points:
From this you can pick out common structures on the map - concentric (ish) circular type lines often represent a hill, such as on the left of the given map. V or U shaped ridges represent an elevated ridge or valley (such as at the bottom of the map, a ridge in this case.)
Some maps such as this one are very helpful in their labelling of certain points, others not so much - but the same points apply regardless. Often you see these sorts of topographical features overlaid on normal maps too to represent elevation - it's very useful to be able to meaningfully read them so you can tell if your route is going to be steep, shallow or somewhere in between (and indeed plan a route as such!)
