Imagine it like putting together a jigsaw puzzle, except that the picture on the front of the puzzle has lots of repeating motifs, so you end up with multiple pieces that look identical. You won't be able to tell how the whole thing fits together, but you can assemble the bits that are well-behaved and unique.
Modern technology gives us larger jigsaw pieces, which allows us to distinguish between almost-identical parts of the puzzle better. But I would note that the project linked did a huge amount of sequencing using very expensive methods to be able to resolve the whole thing.