If you are filing for a dissolution of your marriage in California, and you do not have a lawyer, you can go to the Family Court Facilitator at the courthouse, they will help you fill out the necessary paperwork. Your husband does not need to live in California for you to get divorced in California. You may not be able to obtain any support or property orders against your husband but you can become single. Your husband will need to be served with the pleadings, or he can sign a form called a Notice and Acknowledgement of Receipt.
You can file for a divorce in the county where you live. Your husband does not need to sign anything, but you will need to arrange for him to be legally served with the petition and summons. This can be done by any adult person in his country of residence who then completes a Proof of Service of Summons form, which is filed in your case. If this is in San Francisco County, the local rules also require an affidavit by the person completing the service in a foreign country that includes (a) a physical description of respondent; (b) a statement as to how respondent was identified; (c) the place where service was completed; (d) the address of the person who served respondent; and (e) a statement as to why the person who served respondent was in the country as respondent at the time of service. (San Francisco Local Rule 11.B.3.)
Although his country of residence does not recognize divorce, this country does; you are not required to be a U.S. citizen to have the right to divorce in this country. So long as you have lived in California for 6 months, and in your current county for 3 months, you can file a Petition for Dissolution of Marriage in California, in your local county courthouse.
You do need to arrange for service of the divorce papers on your intended ex-spouse. You can do this a couple ways: he can sign to accept service by mail, which requires his cooperation; you can contact a local attorney service to arrange service; and if that doesn't work, or you don't know where he is, you can ask the court for an order permitting you to meet service requirements "by publication." If it reaches that point, you can get more information on service by publication from the self-help center at your local courthouse (most courts do have them).
It takes 6 months from the date of service of process on opposing party to complete your divorce; that is the law in California. And that is if he does not oppose the divorce - if he does, it can take longer.
I cannot answer any further questions because I would need more information. The expenses can vary depending on whether you qualify for a waiver for court fees, whether you hire an attorney, whether there are assets, kids, etc.
I strongly suggest that you make an appointment with a local attorney who practices family law and offers a free consultation. I am out of your area, so I suggest using this site to locate a qualified attorney who offers a free consult. In the San Francisco area, there should be plenty of attorneys who are willing to meet with you to answer all of your questions and help you get started.