The name "SC-chess" comes from "self-capture", capturing own pieces stated above.
1. (exchange) If you capture your opponent's piece, then put it in your prison. If you and your opponent have captured the same kind of pieces, then they are exchanged "immediately". When you exchange the pieces, put the piece from your prison into your opponent's airfield. It is done by you and your opponent simultaneously.
2. (self-capture) Your non-King pieces can capture not only your opponent's pieces but also your own pieces except a King (self-capture). Your King can capture only your opponent's pieces and not your own pieces. It is likely that non-king pieces can quarrel among friends. Self-captured your pieces are stored in your airfield.
3. (drop) In any turn, a piece in your airfield can be put (dropped) on any* empty square on the board instead of moving your piece on the board, which is considered as one turn. (* An exceptional rule exists for Pawns, below.)
4. (Pawn) A Pawn can not be dropped onto the 8th rank squares. But unlike Hostage chess, it can be dropped onto the 1st rank. A Pawn is always allowed to jump from the 2nd rank to the 4th rank irrespective of it was dropped or not.
5. (promotion) Pawn promotion is performed by exchange. Your Pawn is promoted to any of your pieces except a Pawn, King, and the pieces on the 8th rank. As soon as your Pawn reaches the 8th rank, it goes to the square or your airfield or your opponent's prison where the target piece lives in, and the target piece is dropped onto the square where the pawn located last. This exchange is done before the next turn starts.
6. (others) Castling can be done according to the Orthodox Chess rule. En passant also obeys the orthodox rule, but several notes follows. Your Pawn located on the 5th rank has ability to do en passant capture irrespective of it was dropped or not. The target Pawn is only your opponent's Pawn jumping from the 2nd rank to the 4th rank, not a dropped one directly onto the 4th rank.
The rule 1 is little bit different from Hostage chess, this is more simple. There is no possibility that a bishop and a knight are exchanged. [As a minor variation of rules, it is possible to adopt the same rule as in Hostage chess about the exchange of pieces.]
By those rules, the pieces on the board does not exceed the starting pieces, and there exist reserve pieces out of the board of both black and white, one color ready to use in the airfield, and another waiting for exchange in the prison.
Self-capture gives you another strong method of attack and defence. Exchanging imprisoned pieces gives possibility to drop to both of players, while self-capture gives it to one side. However, it depends on the situation whether self-capture is good or bad for you, because you certainly get a piece to drop, but in many case, your total power on the board decreases temporary.
By the rule 2, the possibility of solving chess problems is little bit greater than the case of Hostage chess. There exist some arrangements where Hostage chess can not checkmate a King, but SC-chess can. Figure 1 is an example. Black has all the rest pieces as reserve ones, while White has no reserve pieces.
[SOLUTION] Nxb6 Ka7 Nxc8 Ka8 R*a7 Bxa7 Nb6 Bxb6 Q*b8 Kxb8 Nc6.
After Nxc8, exchanged Rooks, and then White has a Queen and Rook in the airfield. R*a7 means a Rook from the airfield is dropped onto a7.
There are many choices when you promote a Pawn: which piece to be, where it locates --- on the board, airfield, or prison. It is quite natural to choose the strongest piece in the prison for a promotion target, you can rescue an imprisoned piece. However, there exist some cases that you should promote a Pawn to an on-board piece. Figure 2a shows such a case that the White Pawn E7 should be promoted to the Rook A7, it causes an immediate checkmate (Figure2b). But if the Pawn is promoted to an imprisoned Queen, then the Black Rook C3 moves to C8 (Figure2c), and the White King is mated after several turns.