For accurate information see the actual Regulations for the Prevention of Collisions at Sea (the COLREGS), which are available in several places   on the Internet. Another useful site offers an interactive display and quizzes aimed to teach recognition of vessels at night for potential skippers. The COLREGS comprise 38 Rules and a technical Annex. They cover lights, sounds, display of shapes and some flags, and behaviors of all ships and boats on the high seas and waters connected to them. Countries may make special regulations for inland waters, such as the Great Lakes or canals, and some do. Usually these special regulations extend the COLREGS rather than change them; the COLREGS prohibit displays that might be mistaken for internationally agreed displays.
Let me try to summarize the COLREGS by glossing over details that are not likely to be important in VS. The relevant sections are Rules 1 (general applicability and submarines), 20 (requirement to display lights), 21 (definitions of lights), 22 (visibility ranges), 23 (power-driven vessels), 25 (sailing vessels and vessels under oars), 30 (anchored vessels and vessels aground) and 38 (exemptions), and Annex 1 (positioning and technical details of lights). Rules 24, 26-29 and 31-37 deal with lights for vessels towing, not under control, fishing, dredging, and other special circumstances not so far represented in VS.
I will concentrate on the requirements for boats and small ships. Anybody creating a really large ship for VS (such as Queen Elizabeth II, Monarch or Titanic) should read the actual regulations, especially Rule 22, Rule 23 and Annex 1. I will present this summary as a sequential list of descriptions with guarded headings. Read the headings downwards and when you find the first one that matches the vessel you have in mind, the attached paragraphs set out the requirements. Summary definitions of sidelights, sternlights, and mastlights (called masthead lights in the actual COLREGS) follow the summary of the requirements. [My comments regarding how these requirements may be met in VS are shown as green in square brackets.
The COLREGS did not exist at the time and the vessel should not carry the prescribed lights. It may have had lights determined by other authorities (such as Victory), or may have had no lights so as to be not seen by pirates or victims (such as Roman trading ships or Viking longboats).
No permanent lights need be carried, but a temporary white light must be shown in sufficient time to prevent a collision. An electric torch or a lighted lantern are OK. Such vessels may carry the appropriate lights to small sailing vessels (this covers rowing boats too) if they wish. [A VS boat in this category complies if it has no lights.]
Warships normally carry the lights for vessels propelled by power in peacetime. This includes submarines when on the surface, but US Regulations require them to carry a yellow flashing light as well (3 short flashes over a 3s period, then 3s off before repeating) in US waters since they are not very visible in the water. [This may be difficult in VS.] Aircraft carriers carry their mastlights off-center and this imposes other constraints on their sidelights. [Of course, any warship may decide to travel unlighted for operational purposes but naturally the COLREGS do not approve this action. Some VS warships might claim to be under operational conditions and thus show no lights.]
The vessel must carry sidelights and a sternlight. The absence of a white mastlight signifies that the vessel is under sail. Small vessels of length less than 20m may carry the sidelights and sternlight in a combined lantern at the masthead. Optionally, if a sailing vessel carries the sidelights and sternlight on the hull, it may also carry both an all-round green light and an all-round red light vertically above it at the masthead. [This is rare except on long-distance ocean cruisers which want to avoid being run down by large ships in mid-ocean with inattentive watch officers.]
The vessel must carry sidelights, a sternlight and one or two mastlights. The mastlight(s) signify that the vessel is under power. Large vessels (over 50m) must carry two mastlights on two masts with the after light higher than the forward one (see Rule 23). Vessels under 50m in length may carry a single mastlight, but can carry both if desired.
Small vessels of length less than 12m may use an all-round white light instead of a single mastlight and sternlight. The mastlight or combined light must be at least 1m above the sidelights. [See Annex 1 for heights in other cases.]
Even smaller vessels of less than 7m whose maximum speed is less than 7 knots may carry just a single all-round white light, but sidelights are recommended to be carried as well. [Such slow boats may be rare in VS.]
Note that a vessel under sail but also using an engine is regarded as being under power. In the daytime it should display a black cone pointing down (see Rule 25 and Annex 1), and at night carry the lights for a power vessel. [It may be difficult to do either in VS when a sailboat turns on its engine.]
A single all round white light shall be carried in the fore part of the vessel, and another all-round white light near the stern, but lower than the first light. A vessel of length less than 50m may instead carry a single all-round white light. [It may be hard to dynamically change normal lights to anchor lights in VS.]
A sidelight is visible from straight ahead (0 degrees) to a bearing of 112.5 degrees from the bow. See Screens for how the visibility cuts off. The sidelights on the starboard/port sides are green/red respectively. Sidelights are normally mounted on the hull or close to it. Vessels of less than 20m may combine the two sidelights into a single lantern mounted on the centreline.
A sternlight is visible from a bearing of 112.5 degrees from the bow on one side of the vessel through straight astern to 112.5 degrees on the other side (total of 135 degrees). See Screens for how the visibility cuts off. The sternlight is white. Sternlights are normally mounted on the stern or close to it, or in a combined lantern. Note that typically an observing vessel can see only one of these three lights at a time, unless it is close to a changeover bearing. All three can never be seen at the same time.
A mastlight is visible from a bearing of 112.5 degrees from the bow on one side of the vessel through straight ahead to 112.5 degrees on the other side (total of 225 degrees). See Screens for how the visibility cuts off. The light is white. Mastlights are normally mounted on a mast or a high point on the vessel. Mastlights signify the vessel is under power. [Why are they not visible from aft? Well if you are approaching another ship from that relative bearing, you have to give way regardless of whether it or you are sailing or under power.]
All lights must be visible at the required intensity over the prescribed arc except as described below. This is usually achieved by fitting lights with opaque screens that block the light outside the arc. In real boats, Fresnel lenses and mirrors may be used to increase intensity in the horizontal direction.
Each sidelight must be visible at the required intensity for 1 degree across the bow, but shall cut off (be invisible) by three degrees across the bow. This implies that both sidelights will be seen simultaneously only by a vessel within 3 degrees either side of straight ahead.
The intensity of sidelights, mastlights and a sternlight may begin to reduce within 5 degrees of the side arc limit (112.5 degrees on either side) and must be completely cut off 5 degrees past it.
[VS boats should make a reasonable attempt to meet these limits, but exact compliance may be difficult given the simulated nature of VS lights. However see the page on technical advice.]