By looking at how long it took to mine the last set of blocks. The rate is supposed to be 1 block per 10 minutes so you can estimate the hashing power of the ne

By looking at how long it took to mine the last set of blocks. The rate is supposed to be 1 block per 10 minutes so you can estimate the hashing power of the network by looking at the time taken to solve the last X blocks. If it's too fast, difficulty goes up, too slow and it goes down. The nodes can "agree" without needing to communicate , because they all use the same formula (and share the blockchain) they should all agree on the same answer for what the difficulty of the next set of blocks should be.