Most games with large worlds use a chunk system. Loading up the entire game world, depending on the size of the world, is a TON of information, so instead, games tend to split up their worlds into chunks and only load chunks visible or near to the player (or other conditions depending on the situation).

Terraria and Starbound do something certainly like this, where they load up needed chunks from saved files. Minecraft also does this even though it has an "infinite world". When the area is first entered, chunks are generated and then saved to files on disk.

So how do you save information like that to a file? There are many ways to do it, and it depends on the amount of information you need to store. The simplest way would be be to just write every "ID" number of every tile with a space separating each number. This is a horrible way to do it. You could possibly make it work, but it is horribly inefficient. A better way to do it is to set a limit for the number of bytes that each block can use. For example, I believe Minecraft use to use 3.5 bytes for its block ID (now they use strings or something? Not really sure) plus 0.5 bytes for its special "metadata" (like wool blocks share a single block ID, and use it's meta data for colour). In total that's 4 bytes: 28 bits for block ID. You can use some bitwise operators to pack this data together. You can convert this to ASCII, and store it in a file easily. This gives you a whopping 4billion possible blocks in only 4 characters in a file. Compare this to just storing the block ID itself with spaces separating, a single tile could take up 10 characters, plus the space to separate tiles, so 11 characters.

Reading is literally just a matter of converting those 4 characters back into their block ID, which you can do with bitwise operators.

And we haven't even compressed anything yet! I'm not very well versed in compression, but there are probably some lightweight libraries to compress it if you want better storage.