Weather routing relies on one key factor, the accuracy of the forecast. Forecasts have improved greatly, but they are not always perfect. This is why it is important that you learn how to interpret the weather maps yourself and furthermore, know how to apply this knowledge to the real world to choose a safe route that will avoid deleterious weather.
These two maps are of the same region and the same time. They also show some important concepts that will play into your interpretation of the maps.
First, in the Northern Hemisphere, wind rotates clockwise around a high pressure system and anti-clockwise around a low pressure system. Second, the closer the pressure gradient (isobars) are to each other, the more powerful the winds will be.
A simple way to think about it all is to imagine the earth as a sandbox where an evil kid is tormenting the landscape. The kid has two tools of destruction at his disposal: a vacuum and a fan. The vacuum pulls air up, and the fan pushes air down. He can't use both in the same place, so he is forced to use them next to each other. Air from the fan smashes down onto the sand while the vacuum draws air up from the sandy floor. You are an unlucky ant who is trying to get across this epic sandbox of doom, all while avoiding the menacing child.
The fan is a high pressure system and the vacuum is low pressure, if you are close to either, the conditions are brutal, but if you keep a safe distance from either, you find that you can survive the torture.
Just as the ant can see the fan and vacuum from the surface of the sandbox, you too can see the fan and vacuum from the surface of the sea, as they are told to you in the form of clouds. Reading clouds is a very valuable skill to have and one that will be discussed in much greater detail.
A barometer can let you know what your current air pressure is, which then would give you an idea about where you are in relation to the fan and vacuum and understanding how the pressures work will let you stay at a safe and comfortable distance from either centers.
Knowing that winds blow clockwise around the center of a high pressure, if you are going downwind you can then easily tailor your position on the ocean for the most comfort by simply turning to starboard (towards the high pressure) for less wind or to port (towards the low pressure) for more wind. Riding the pressure gradients over the ocean will get you there safely and calmly without the need for fancy weather routing software.
Now, why not use the fancy and expensive electronic gizmos that will tell you exactly where to go? Because they don't always work as well as touted.
Routing software depends on an accurate forecast, and that is the weak point in this story. The software will tell you how to sail the best in the world they are presented with, the sad thing is this is rarely the same world you live in. By looking at the sky you can see what the weather is right where you are and looking at the barometer tells you what the atmospheric pressure is in your column of air.
Weather forecasts are great for deciding when to go out to sea, but once you are out there, their utility quickly diminishes as they are no match for the accuracy of the visible sky around you.