According to Reddit user MegamanJB, some of the Spelljammer ship rules can be made out on the DM Screen preview image. They transcribe what they could make out, which includes Ship Encounters, Ship-Ship Starting Distance, Crashing, Shipboard Tasks, Ship Quirks, and Ship Cargo.
Ship Encounters
d100 - Ship Encounter - Attitude Roll
Distance - Notes
Size of Creature or Object - Bludgeoning Damage
d12 - Task
d10 - Quirk
d100 - Ship Encounter - Attitude Roll
- Bombard Leviathan? captained by... (giff warlord) and ... giff shipmates and 3...
- ... captained ... explorer
- Scorpion ship Claws of... captained by H... (hobgoblin captain) and crewed by 1 bugbear (first mate) 8 hobgoblins and 2 hobgoblin priests
- Shrike ship... captained by Yaj (githyanki...) and crewed by 11 githyanki buccaneers.
- Space Galleon ... captained by K... (beholder) and crewed by 1 spectator (first mate), 3 cult fanatics and 16 cultists
- Space Galleon ... captained M... and crewed by 1 invisible stalker (first mate)... aarakocra and 7...)
Ship-to-Ship Starting Distance
At the start of an engagement...Distance - Notes
- 250 ft: Long range for... light ... and heavy crossbows.
- 500 ft: Long range for... and for... crossbows
- 1000 ft: Beyond the range of most ranged weapons
Crashing
When a malfunctioning ship crashes into a creature or an object that would presumably damage it....Size of Creature or Object - Bludgeoning Damage
- Large: 4d10
- Huge: 8d10
- Gargantuan:
Shipboard Tasks
During the uneventful part of a voyage...d12 - Task
- 1 - Scrape ... off the hull
- 2 - Scrub ... and dishes in the galley
- 3 - Chop vegetables in the galley
- 4 - Swab the deck...
- 5 - Update the ship's navigational charts which require cartographer's tools.
- 6 - ... the captain's ...which requires ... tools.
Ship Quirks
Roll on the Ship Quirks table if you want to add a bit of "personality" to a ship.d10 - Quirk
- 1 - A chatty ... haunts the cargo hold.
- 2 - The ... of the hull echoes throughout the ship.
- 3 - Any creature that ... itself from the ship's ...
Ship Cargo
To randomly determine what's on the cargo... of a spelljamming ship... If a cargo container is... a character can try to unlock a container using thievery tools doing so with a successful DC 20 dexterity check.Cheap Cargo
d12 - CargoExpensive Cargo
d12 - Cargo- 1 - Crate containing fifty blank ... books (50 gp each)
- 2 - Crate containing one hundred ... bottles of ink (10 gp each) and one thousands ... (1 gp each)
- 3 - Crate containing hearty portions of ... flasks of... (50 gp each)
- ...
- 12 - kegs of gunpoweder ... (see "Explosives" in the Dungeon Master's Guide)