In duplicate bridge, what is the penalty for someone bidding out of turn? Specifically, opening the bid by accident while sitting to the right of the dealer.
Here is a summary of the relevant rules that @Pieter Geerkens linked to. I am leaving out some of the more sophisticated points, for example, the fact that an artificial/conventional pass call is treated as a bid for the purposes of these rules. The guiding principle is not to punish the out-of-turn bidder, but to make it impossible for the offending team to benefit from the information improperly exchanged. That's why many of them refer to Law 23, which allows a TD to further adjust the score if it is determined that the offending team gained an advantage by the improper call.
In most cases, a bid on LHO's turn is treated as a change in call, which is treated separately. In practice this is a difficult mistake to make--you don't usually make two bids in immediate succession.
Pass out of Turn
Bid out of Turn
Double / Redouble out of Turn
Here are the relevant rules for the various scenarios under your questions:
LAW 30 - PASS OUT OF ROTATION
When a player has passed out of rotation and the call is canceled, the option in Law 29A not having been exercised, the following provisions apply (if the pass is artificial, see C below): A. Before Any Player Has Bid When a player has passed out of rotation before any player has bid, the offender must pass when next it is his turn to call and Law 23 may apply. ...
LAW 31 - BID OUT OF ROTATION
When a player has bid out of rotation, has passed artificially or has passed partner’s artificial call (see Law 30C) and the call is canceled, the option in Law 29A not having been exercised, the following provisions apply: A. RHO’s Turn When the offender has called at his RHO’s turn to call, then: 1. if that opponent passes, offender must repeat the call out of rotation. When that call is legal there is no rectification. 2. if that opponent makes a legal* bid, double or redouble, offender may make any legal call. When this call (a) repeats the denomination of his bid out of rotation, offender’s partner must pass when next it is his turn to call (see Law 23). (b) does not repeat the denomination of his bid out of rotation, or if the call out of rotation was an artificial pass or a pass of partner’s artificial call, the lead restrictions in Law 26 may apply, and offender’s partner must pass whenever it is his turn to call (see Law 23). ....
LAW 32 - DOUBLE OR REDOUBLE OUT OF ROTATION
A double or redouble out of rotation may be accepted at the option of the opponent next in rotation (see Law 29A), except that an inadmissible double or redouble may never be accepted. If offender’s LHO nevertheless calls, see Law 36. If the call out of rotation is not accepted, it is canceled, the lead restriction in Law 26B may apply and: ... B. Made at RHO’s Turn to Call If a double or redouble out of rotation has been made when it was the offender’s RHO’s turn to call, then: 1. if offender’s RHO passes, offender must repeat his out-of-rotation double or redouble and there is no rectification unless the double or redouble is inadmissible, in which case Law 36 applies. 2. if offender’s RHO bids, doubles or redoubles, the offender may in turn make any legal call, but offender’s partner must pass whenever it is his turn to call. See Law 23 if the pass damages the nonoffending side.
LAW 23 - AWARENESS OF POTENTIAL DAMAGE
Whenever, in the opinion of the Director, an offender could have been aware at the time of his irregularity that this could well damage the non-offending side, the Director shall require the auction and play to continue (if not completed). When the play has been completed, the Director awards an adjusted score if he considers the offending side has gained an advantage through the irregularity*. * As, for example, by partner’s enforced pass.