Okay, so I am assuming you have done the basic tutorial missions. You haven’t? Well, do them! No arguments. They teach you the basic basics. What’s the difference between this and those? The same difference between driving lessons and road experience. One gets you a licence, the other keeps you alive afterwards.
The Galaxy Map is not just a "you are here" diagram of the Milky Way. You can do a lot more than just plot routes. It shows the location of stored ships, mission related destinations, friends online and gives you the ability to search for systems by economy, population, star type and allegiance.
I want to find a high tech station
There are third-party websites (such as eddb.io) that use crowd-sourced data to show where ships and modules may be found, but the Galaxy Map gives you the ability in the game, to a lesser degree. It can’t tell you that a station has a particular module or ship in stock, but you can find the most likely candidate systems in short order.
To do this, you open the Galaxy Map and on the View TAB, select the Map icon. This offers a selection of categories to map. We want "Economy" here. This shows the different types of economy in the galaxy. We want to select just "High Tech" and "Refinery". Below the list is another filter option, select "Population" here and slide the "minimum" selector past half-way. You should now only see star systems of High Tech and Refinery economies with large populations. And well stocked Shipyards and outfitting…
Running low on fuel? Find scoop-able stars!
Again, open the Galaxy Map and on the View TAB, select the Map icon. This offers a selection of categories to map. We want "Star Type" here. This shows the different types of star in the galaxy. We want to select just types "A, B, F, O, G, K and M". You should now only see stars you can fuel scoop. Very handing for panic refuelling on a long route, when you cannot make the next plotted jump, but there’s a nearer scoop-able star.
Have bounty from Alliance and you’re in Federation space?
In the Galaxy Map and on the View TAB, select the Map icon. Select the allegiance category and only select the faction you want to find. You should now only see systems they control. You can then plot a route to the nearest and hand in that 300,000CR that has been burning a hole in your Transactions TAB for a week!
So you can see, without me demonstrating every use, that the Galaxy Map is a vital source of in-game information.