I live in Florida but work for a company in California. California imposes a state disability tax and unemployment tax. Since I am a non-resident, do I have to pay it, and if not, how do I get my money back?

Assuming that you do not WORK in California, the CA SDI and SUI taxes do NOT apply to you.

If your employer is withholding these taxes, ask them to cease and to arrange for a refund on your next paycheck. They will probably need to contact the California Franchise Tax Board for guidance, but it is easier for them to arrange for the refund than it is for you.

Unless you are a resident of CA or you are actually present in CA to do the job, your income is not subject to CA taxes. You do not pay CA SDI.
Follow what AtlantaTaxExpert has suggested.