While the metaphor of an Iron Curtain was made literal with the Berlin Wall, surely it wasn't too hard to simply travel across East Germany and walk into the west?
It actually was very hard. The entire border was secured by a fence, mines, watchposts, patrols etc. No one was allowed to even come close to the border, people living near it were relocated. There were only a few rail lines and highways connecting West Germany with West Berlin, but no easterner was allowed on them and there was basically no way to get on or off while in transit. You also have to keep in mind that you couldn't really travel that far from where you lived without attracting attention. Of course some people made it across, mostly via the Baltic sea or the less ironclad border between Austria and Hungary. But it was very hard to pull off successfully.
If you're interested in a book about life on the Inner German Border, I'd suggest Daphne Bergdahl's Where the World Ended. It's a book about life in the Thuringian village of Kella which was located inside the Schutzgebiet, the 500 meter wide restricted zone that ran the entire length of the border (this is the one directly adjacent to the border, contained within the larger Sperrzone, which was 5 km wide). A single road led into the village, which was otherwise surrounded on three sides by the border walls.
She goes into some detail about the fortifications on the border, but spends much more time on life in the village and the forms of everyday resistance the villagers practiced against the regime while also comparing that with the Ostalgie (nostalgia for the old East - in German Ost - Germany) many villagers felt after the Wende. Highly recommend it!
Edit: added the maps link, because why not?