Rules for Starting Positions
According to our good friend Wikipedia, there are two restrictions for the starting position, both of which seem rather obvious: the bishops must be on opposite-color squares, and the king must be placed between the rooks.
Castling
I find castling a bit tricky in Chess960. The confusing thing about castling in Chess960 is that even though the king and rooks are typically not in their standard position, the rules for castling remain pretty much the same as in standard chess, which can lead to weird stuff--sometimes you can even castle and have only one of the two pieces change positions, or have the king and rook move many squares at once!
The key thing to remember when castling in Chess960 is that the resulting king and rook position is exactly the same as in standard chess. This means that castling a-side (as it's called in Chess960) leads to the king sitting on c1 (or c8) and the a-side rook sitting on d1 (or d8), while castling h-side leads to the king sitting on g1 (or g8) and the h-side rook sitting on f1 (or f8). As in standard chess, you cannot castle if a square in the king's path is attacked or occupied by a piece, or if the destination square for the king or rook is occupied by a piece. Note that just like in standard chess, a-side castling is notated O-O-O, and h-side castling is notated O-O.
I suppose the mechanics for castling online depends on the specific website, but on lichess, you can castle in Chess960 by dragging the king to the rook with which it wants to trade sides. Here's an example game in which I tried to castle but it all went wrong: rather than dragging the king to the rook, I dragged the king to its intended destination square, which was interpreted as a normal king move. On move 5, I tried castling a-side, but I played 5. Kc1?:
Stockfish evaluates the position has having gone from about +0.5 (a half-pawn advantage for White) to about -1.7 (nearly a two-pawn disadvantage for White!) after 5. Kc1. In fact, following this mishap, the rook on a1 didn't get to enter the game until move 32:
Popularity
On December 16, Chess960 was the most popular of non-standard chess variants on lichess, even ahead of UltraBullet, which is standard chess with an extremely fast time control. This table shows the number of people who played each variant this week:
It's clear that non-standard chess variants are much less popular than standard chess variants (which vary only in their time controls), but Chess960 fares well relative to other non-standard variants.
Seeing Chess960 in Action
If you want to see Chess960 in action, you can take a look at the top-rated Chess960 game on lichess being played right now on LichessTV.
You can also take a look at my most recent stream on Twitch, in which I played the daily Chess960 tournament (5-minute games)... I played a total of 9 games and finished 9th (win rate = 56%, performance = 1880):
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