CA does not have a true expungement process - i.e. erasing the conviction from your record. The best you can do is a post conviction dismissal. You should first ask if your conviction is eligible to be reduced to a misdemeanor. If so, you want to make that motion first, then petition for the dismissal. An attorney is not necessary for this, but if you want to make sure things are done right consult a local attorney.
Mr. Feasel is a former prosecutor in San Mateo County (CA) with over 10 years of criminal law experience. Nothing stated on this site shall in anyway be construed as legal advice, or as creating any attorney/client relationship. If you would like to hire Mr. Feasel to further investigate your situation, feel free to contact him thru this site.
What Mr. Feasel says is correct. I would only add that if your conviction was reduced to a misdemeanor that this would lift your gun restrictions, making this much more important than the expungement itself.
Based on the information you provided, there is a good chance you can have it reduced to a misdemeanor and then dismissed pursuant to Penal Code 1203.4.
The process in itself is not difficult, but courts overwhelmingly prefer a lawyer handle these proceedings. Unfair, but sometimes just having a lawyer there makes it happen.
I would recommend speaking with a reasonably priced local attorney to help you.
Expungement, which is actually a dismissal pursuant to Penal Code section 1203.4, does not restore the right to possess a firearm. However, expungement does allow you to state on job applications that you are not convicted. As several other attorneys have answered, in order to possess a firearm you need to reduce the felony. In order to have your felony reduced the offense must be a wobbler and you must not have been sentenced to a prison sentence, even if it was a suspended sentence. To see if the offense you were convicted of is a wobbler and eligible for reduction you must look up the code section that you were convicted of. If you do not have that code section number then you can get it from the court. After you have the section number you were convicted of you can call my office and we can inform you whether your offense is a wobbler and eligible to be reduced. By reducing the felony, the firearm possession ban will be lifted. However, applying for a CCW permit is a separate process. You must apply with the county sheriff or your local municipal police department and show good cause for the permit.