In California Superior Courts, what would be some common grounds to ask the judge to sanction the opponent party?
Under what circumstances would such motions be granted, and how often do any such motions presently succeed?
While there are certainly statutory and procedural vehicles for sanctions, they are almost never requested or allowed when moved for, and are almost never imposed by judges. Something very severe needs to occur and not just your typical discovery violation ("speaking objections" during depositions, being late with responses, failure to cite to affidavits, affidavits citing conjecture rather than fact, et). It would have to be something quite serious....like misleading the court or directly failing to comply with a direct order or ruling on a motion. It is exceedingly rare. It is most seen in Federal Court.
Sanctions are available in most or all U.S. courts, including California. There are various statutory and rule-based justifications; however, these motions are rarely brought by licensed attorneys, because the standard for sanctions is generally high. They are more often brought by and against pro se parties, whose grasp of the rules tends to be more tenuous.
Yes, parties can file motions for sanctions. In civil cases, this is one of two ways sanctions can be imposed, the other being the court filing a motion under its own authority (Rule 2.30(c)). Likewise, sanctions under the Code of Civil Procedure, section 128.7, refers to a motion for sanctions by the opposing party. The fact that they say "sanctions may only be imposed upon [among other things] a motion by a party" (rather than "a party may file a motion for sanctions") indicates that the normal rule is that when sanctions are allowed, a party can move to impose them (this is, in fact, the case).
Sanctions are granted when a party violates court rules or disobeys court orders. The motion specifies what rule they violated, and the other party can respond, and if the judge finds they broke the rules sanctions can be imposed.