Many good answers here, and some contradictory ones. There seems to be some disagreement about whether heaving to, or keeping the bow into the wind is better, or whether running with the wind under bare poles or a storm headsail is safer.

Running would be safer in most circumstance, as long as there was sea room to leeward. (Being caught off a lee shore in a hurricane force storm was very dangerous.) Running would be especially beneficial if your ship was in the "safe quadrant" (to the left of the track of the hurricane in the Northern Hemisphere - reversed in the Southern), as running before the wind would take you out of the path of the storm, and into lesser winds and calmer seas.

One preparation which might be made, if there was enough warning of the building storm, and if the crew were large enough to accomplish it safely, would be to strike the Royal and T'gallant yards, and the T'gallant masts, as this would reduce weight and windage aloft.

Given that the age of sail spans human history up until say 1840 or so, that's a broad question :-) but generally, stay stern to the winds, either by setting a small headsail or a stern anchor; batten everything down, and pump constantly. In the northern hemisphere, if possible, try to steer south and slightly west to stay out of the path of the intense winds.

For the most part there would always be crew on deck standing watch with at least one officer. If it got bad enough they would wake up the rest of the crew. Occasionally you could lash the helm fast but that meant that you would be in trouble if you had to use it suddenly.

What would happen though would be that men aloft would be brought down to the deck for safety and sails would be reefed and brought in.

Your options were usually either to run before the storm or head up into it. Running isn't a bad option but waves breaking over the stern and sudden changes could be problematic and dangerous. Heading up into the storm will be rougher but retain a larger degree of control over the ship and the helm. For both you would have a minimum of sails out, a jib or two and everything else reefed or brought in.

The goal is to not be taking the waves broadside, and ships are designed to take them on the bow.

This really hasn't changed in modern times. Even in modern ocean racing there will always be someone awake on deck in case of an emergency.

Trying to find an old book that describes some of it in the context of the USN in 1812, but Ive also taught beginner sailing and raced including a few Annapolis to Bermuda trips.

If sailing just wasn't an option then yes, drop the sea anchor, leave a small headsail up, leave a skeleton crew above to keep an eye out(they would likely tie on to something) and pray. But ships and crews throughout history can be remarkable resilient and take a beating from the elements.

unfortunate soul required to remain topside to steer

yes, storm watch is generally 30 minutes on the helm as opposed to 4 hours, but when conditions get to that point heave to or lay a hull are the options.

Running before high winds is madness, it is incredibly difficult to maintain the helm whilst running and a gybe will destroy the rigging, I would never consider running before anything above a force 8. At force 12 the deck would be unmanned due to the inability to breath the air, it's full of sea foam by that time.

A hurricane is very predictable and can be used to make a passage faster, some captians of old were notorious for making their passengers suffer mal du mer due to the penchant for skirting hurricanes to use the winds.

Source, traditionally rigged sloop sailor.