In part 1, I laid the groundwork for what I consider to be a sandbox playstyle. I'd planned on getting into how to work cape-and-sword tropes into a sandbox, but as I started writing it, I found I was introducing all sorts of other baggage regarding how sandboxes work in actual play, so I want play porter for a moment and clear those bags out of the way first.
There are a number of features common to sandbox settings, and, judging from the many discussions in which I've participated on various gaming forums over the years, it seems that every one of them comes with some misunderstandings attached.
First, a sandbox game-world is not tailored, to use the 3e D&D DMG parlance, to the adventurers. In the game-world, there are hazards and challenges that will be easy for the adventurers to handle, some that carry a measure of risk to the adventurers, and some which the adventurers are unlikely to overcome unless they are extremely clever and insanely lucky. Sandboxes include a wide range of degrees of difficulty in challenges, hazards, and encounters, and the adventurers may face them at any time, with or without warning - in fact, one of the important elements of game-play is gathering intelligence on the nature of hazards which exist in the game-world, to reduce the risk of an unexpected, overwhelming encounter.
Second, a sandbox typically contains a number of adventure sites - a ruined castle, a creepy abbey, a dark forest, a maze of caverns, a keep on the borderlands, and so on. Scattered throughout the game-world are clues - rumors picked up from travellers in taverns, books found in dusty libraries, a map found in a dead bandit's pocket, a murak painted on the wall of a monk's cell, et cetera - which point the adventurers in the direction of these locations. These locations typically receive more attention than other places in the game-world during the referee's prep, and are often intended to have an element of replayability about them - each supports multiple visits by the adventurers. Clues are enticements to the adventurers, tempting them with the means to achieve their goals, or even satisfying a goal itself.
Third, a sandbox offers the opportunity for the adventurers to explore at their own pace and in a direction of their choosing. Hexcrawls - exploration hex by hex across a map - are strongly associated with this, appearing early in the hobby in published settings like Blackmoor, the Wilderlands, and the Spinward Marches. This sometimes implies that sandboxes need to be extensive, but that isn't necessarily the case (qv, Keep on the Borderlands).
Fourth and last, a sandbox should be a dynamic game-world. The 3e D&D DMG associates the term "status quo" with sandbox adventuring, implying a sort of stasis state which is only broken by the presence of the adventurers. A sandbox, however, usually contains non-player characters with agendas they pursue independently of the adventurers, unless or until the adventurers choose to become involved or are swept up as a consequence of an npc agenda coming to fruition. In a well-run sandbox, there are also large-scale events which occur in the setting, such as wars, plagues, and so forth, which again exist independently of the adventurers.
Okay, with those trunks and valises stowed, now I can move on to the swashbuckling in part 3.