if you leave your king on ckeck once the arbiter will warn you. if you did that two more times then your opponent can report it to the arbiter and he/she can claim win.
Touch move...open check

Shine5's answer is incorrect for USCF tournaments.
If you touch a piece, and you're in check, you have to interpose with the piece you touched, if possible. If not possible, there is no penalty.
If you actually make the illegal move and release the piece, your opponent can get the tournament director to penalize you 2 minutes (or 1/2 remaining time) on your clock, in addition to forcing you to move whatever piece you touched.
At no point in a standard tournament do you lose immediately if you make an illegal move.
Blitz tournaments are different. Your opponent can simply capture your King in these tournaments and win the game that way.

Shine5's answer is incorrect for USCF tournaments.
If you touch a piece, and you're in check, you have to interpose with the piece you touched, if possible. If not possible, there is no penalty.
If you actually make the illegal move and release the piece, your opponent can get the tournament director to penalize you 2 minutes (or 1/2 remaining time) on your clock, in addition to forcing you to move whatever piece you touched.
At no point in a standard tournament do you lose immediately if you make an illegal move.
Blitz tournaments are different. Your opponent can simply capture your King in these tournaments and win the game that way.

If a player makes an illegal move in a USCF-rated tournmemt game (using any time control slower than G/29), the illegal move must be retracted, and 2 minutes is added to the opponent's clock.

actually the first game I played otb.
a player said checkmate to me by moving his queen.
however he didn't notice he was in check himself.
so the TD told him to use his queen to block the check this forced him to resign as he lost his queen.
"touched piece must be moved if you can"
he thought I was supposed to say check.

In a live tournament, what is the penalty when you touched/moved a piece but leaves your king open check?
In chess, it depends on the organization. FIDE has different rules than USCF. Seeing as that you are from the United States, I'm going to guess you are talking USCF. Differences with FIDE are below:
If you touch a piece, you must move it if you can. So, let's say you make an illegal move with your Queen because it leaves your King in check. Your opponent stops the clock, gets a director, and he is awarded 2 minutes, and the player that made the illegal move must take back the illegal move, and if he has a legal move, stupid as it may seem, he must play it due to the touch-move rule. So if White does Bd1-b3+, with your King on g8, Queen on e7, and nothing on the a2-g8 diagonal except White's Bishop and Your King, then you must move the Queen to either e6 or f7, no matter how stupid those moves look, you touched your Queen, you must move it if it has a legal move.
Difference between USCF and FIDE: For each violation of legal moves, the USCF rewards the other player with 2 minutes and play resumes, even if it occurs 10 times (20 total minutes). For FIDE, 2nd illegal move is a forfeit. In addition, with USCF, if you push a pawn to the 8th rank and don't PHYSICALLY make it a piece (saying "Queen" is not a legal promotion), then the opponent can just slap the clock back until they make it something. White can not tell Black to make it a certain piece. If White promotes the pawn, WHITE must place the promoted piece on the square. In FIDE, pushing a8 as White or b1 as Black and leaving it a pawn is deemed an illegal move, counts as an illegal move (so if it's your second illegal move of the game, you forfeit), and opponent is awarded 2 minutes, and then you MUST make it a Queen, even if that means stalemate. You must put the piece on the board and not just declare. Also, an upside down Rook is a ROOK in FIDE, NOT A QUEEN! If you need another queen and can't find one, stop the clock and get an arbiter.
As for announcing check, it's actually WRONG to say check in tournament play, and if it is requested that you cease to announce check, and you continue, a penalty can be imposed.

In chess you CANNOT make illegal moves. Therefore you CANNOT leave your K in check.No penalty for that. Now, if you keep breaking good behavior rules, you may have to refer to the Tournament rules and regulations. This is how I handled the situation in my tourneys.
I believe that (at least by USCF rules) that if you make an illegal move AND PRESS THE CLOCk you lose two minutes. (OF course in blitz, you lose).

in the club I played if we played 5 minutes each games and you left your king in check we could capture the king but that was a club rule.

So in other words, there is no set "universal rule" regarding an illegal move. It all depends on the types of games played, organizations, or arbiters discretions.

As for announcing check, it's actually WRONG to say check in tournament play, and if it is requested that you cease to announce check, and you continue, a penalty can be imposed.
Where does it say that in the rules? Just curious, that's all.

So in general, touch move rule doesn't really apply when an illegal move such as leaving king open check and is only subject to various penalty (if any) within the established tournament rule.

In a live tournament, what is the penalty when you touched/moved a piece but leaves your king open check?
In chess, it depends on the organization. FIDE has different rules than USCF. Seeing as that you are from the United States, I'm going to guess you are talking USCF. Differences with FIDE are below:
If you touch a piece, you must move it if you can. So, let's say you make an illegal move with your Queen because it leaves your King in check. Your opponent stops the clock, gets a director, and he is awarded 2 minutes, and the player that made the illegal move must take back the illegal move, and if he has a legal move, stupid as it may seem, he must play it due to the touch-move rule. So if White does Bd1-b3+, with your King on g8, Queen on e7, and nothing on the a2-g8 diagonal except White's Bishop and Your King, then you must move the Queen to either e6 or f7, no matter how stupid those moves look, you touched your Queen, you must move it if it has a legal move.
Difference between USCF and FIDE: For each violation of legal moves, the USCF rewards the other player with 2 minutes and play resumes, even if it occurs 10 times (20 total minutes). For FIDE, 2nd illegal move is a forfeit. In addition, with USCF, if you push a pawn to the 8th rank and don't PHYSICALLY make it a piece (saying "Queen" is not a legal promotion), then the opponent can just slap the clock back until they make it something. White can not tell Black to make it a certain piece. If White promotes the pawn, WHITE must place the promoted piece on the square. In FIDE, pushing a8 as White or b1 as Black and leaving it a pawn is deemed an illegal move, counts as an illegal move (so if it's your second illegal move of the game, you forfeit), and opponent is awarded 2 minutes, and then you MUST make it a Queen, even if that means stalemate. You must put the piece on the board and not just declare. Also, an upside down Rook is a ROOK in FIDE, NOT A QUEEN! If you need another queen and can't find one, stop the clock and get an arbiter.
As for announcing check, it's actually WRONG to say check in tournament play, and if it is requested that you cease to announce check, and you continue, a penalty can be imposed.
Woah!!! I didn't know that placing a rook upside down is illegal, and you can win if the opponent does that!!!
In a live tournament, what is the penalty when you touched/moved a piece but leaves your king open check?