Copyright (c) 1999 Steve Meyers 

Trellis is played on an empty 15x15 checkered square board:

TURN - On each turn, each player drops 2 stones, which must be exactly three cells apart, in either an L-shape (i.e., the chess knight's jump) or in a straight line.
It's allowed to drop just one stone, and it's allowed to pass.
MIRROR - It is not permissible to "mirror" the opponent's moves ten or more turns in succession.
PIE RULE - Player 1 plays two moves for Black and one move for White (a move can consist of up to two stones, of course). Player 2 then decides which side to take, with White to move.
CONNECTION -  Two stones of the same color are considered to be connected if they're orthogonally adjacent, or if they're diagonally adjacent over a "home square"
Black's home squares are the dark squares, and White's home squares are the light ones.
GOAL - Black tries to connect the top and bottom sides of the board, and White tries to connect the left and right sides. A corner point is considered to belong to both sides that meet there.
An example

The black stones are totally connected, while the marked white stone is not, since the diagonal connection is over a square which is not its home square.

Valid distance between the two stones

After the first stone is dropped, the second stone can only be dropped at one of the green dots.

Some words from the author: Note that the standard pie rule is encapsulated within the [game's pie] rule, because it is permissible to pass a turn. (I.e., Player 1 could play one move for Black, then pass for White, then pass for Black.)

Much more information, including Trellis' history, can be seen at Meyers' website.