I am often asked about expungements (PC1203.4)
To be eligible for relief pursuant to Penal Code 1203.4 (expungement) you must successfully complete probation. Assuming you have done so and paid all fines then you are eligible.
There are two ways to seek an expungement. You can do it yourself by filling out a judicial counsel form, submitting it to the Probation Department, and paying a fee (I believe $125). The Probation Department will review your criminal record and assuming you have no additional criminal charges pending and successfully completed probation a judge should grant the motion. The second option is to hire an attorney to prepare a formal Expungement Motion. The fee will substantially more than $125 however.
After you successfully expunged your criminal conviction, if a private employer asks if you have ever been convicted of a crime, you can respond with "No." Most federal and California government applications however, ask you, under penalty of perjury, if you have ever had a case expunged or cleared from your record, and you have a duty to answer this truthfully. Also, if you are applying for public office or a state license (i.e. real estate, doctor, lawyer, stockbroker, etc.) you must disclose the conviction. Even so, the fact that a court found good cause to expunge your conviction weighs in your favor.
Also, as far as the DMV is concerned the conviction will remain and if you are convicted of a DUI within 10 years of the arrest for your wet reckless case the new DUI will be considered a second offense.