Expungement (California Penal Code section 1203.4) is a process by which, following the succesful completion of court probation (satisfaction of all court-ordered responsibilities and penalties, and no new arrests or convictions), the Court will allow the Defendant to petition to withdraw a previously entered guilty plea, at which point that case can be dismissed in "the interests of justice" (Penal Code section 1385).
The expungement petition must be prepared and served on the court and prosecuting agency. The processing of the petition may be accomplished through an internal review by the court, or at an in-person hearing requested and attended by the Defendant and/or his California drunk driving defense attorney. The administration of the request typically takes two months to decision. Presentation of the petition may be done by the completion of a standardized form, or by an individually tailored supporting papers justifying the DUI expungement.
Expungement will formally erase the DUI conviction from your employment record, but may still be discoverable by employers with access to "cached" or archived versions of California's criminal "rap sheets" (conviction records). Expungement does not affect prosecutorial records, so a defendant's prior, although "expunged," conviction may still be a basis for enhancing penalties on subsequent, or repeated, offenses.
The granting of an expungement is not a "given" in the politically charged atmosphere of DUI prosecution and defense on Los Angeles and Orange County Courts. Your best prospect of success in this regard is in the services of counsel dedicated to the unique practice of driving under the influence law.