The first and foremost piece of information all bitcoin holders should know is that in the event of a hard fork that splits the blockchain, bitcoins you possess will be perfectly safe.
Over the past year or so hard forks have gotten a bad reputation for political reasons, but in actuality, most types of forks are merely protocol upgrades. A blockchain split occurs during a hard fork which in turn branches the chain into two parts. If this happens, there is nothing a bitcoin holder has to do but wait and watch the fork unfold.
The folks at the subreddit r/btc have compiled a very well written frequently asked questions post concerning protocol upgrades and how users are affected. The thread gives details about the hard fork process and what to expect.