Gothic 1 Remake drops you into the colony with no mini-map, no compass, and no quest markers. The world map exists, but you have to earn it the old-fashioned way by tracking down a seller and parting with ore nuggets. The man you want is Graham, and he sets up in the Old Camp.
Quick answer: Buy a map from Graham in his hut just right of the Old Camp's main entrance. The Map of the Colony costs 34 nuggets, and the Map of the Old Camp costs 35 nuggets.

Where to find Graham, the map seller in the Old Camp
Graham lives inside a hut positioned to the right of the Old Camp's main entrance. He is the only vendor who sells the paper maps, so there is no alternate source to chase.
You will usually hear about him before you ever reach the camp. Diego mentions Graham on the way in, and a pair of hunters from the New Camp also bring him up during the early road segment toward the Old Camp. Following that dialogue points you straight to his door.

Map prices and which one to buy
Graham stocks a small selection, but two items matter for navigation. One covers the Old Camp itself, and the other is the closest thing the game offers to a full world map.
| Map | Cost | Covers |
|---|---|---|
| Map of the Colony | 34 nuggets | The wider colony, used as a rough world map |
| Map of the Old Camp | 35 nuggets | Layout of the Old Camp area |
If you only want one, the Map of the Colony is the more useful pick for getting between camps and orienting yourself in the open world.
How to buy or take the map
Step 1: Travel to the Old Camp and head to Graham's hut just inside the main entrance on the right. Open dialogue with him to view his wares.
Step 2: Select the Map of the Colony or the Map of the Old Camp and pay the ore nugget cost. The map then sits in your inventory and can be opened whenever you need it.
Step 3: If you are short on nuggets, you can intimidate Graham into handing over a map for free. This works, but it permanently sours his attitude toward you, and he becomes a helpful ally in later quests. Paying him is the safer choice.

How useful the map really is
The map gives you a general sense of where places sit, but it stops being much help after a few hours. It does not track NPCs and it does not update with quest objectives, so you cannot lean on it the way you would in most modern games.
Where it earns its keep is simple route-finding, like remembering the path from one camp to another or locating the arena inside the Old Camp. Beyond that, you will rely far more on listening to NPC dialogue before a quest and on exploring the world yourself. On a second playthrough, many players skip the purchase entirely unless a fetch quest specifically asks for a map to hand to another character.
However you obtain it, you will know it worked when the Map of the Colony or Map of the Old Camp appears in your inventory and opens as a viewable paper map. From there, treat it as a light reference and let dialogue and patience carry you the rest of the way.