How do I monitor the status of a Geth sync in fast mode?

Input this command (vary the datadir to reflect your system if necessary)

sudo geth attach --datadir /var/lib/goethereum/

then at the > prompt type eth.syncing

You'll see something like the output below -- it's the distance between the top two numbers that show how far away you are from synched.

{
  currentBlock: 11767544,
  highestBlock: 11790961,
  knownStates: 628485238,
  pulledStates: 628485238,
  startingBlock: 11790248
}

A response of "false", unintuitively, means you're all good and synched up.