Why hasn't s/he filed an I-130 for you?
Did you make a legal entry, i.e. with a passport through border patrol?
Because you are the spouse of a US citizen s/he can file the I-130 for you.
IF you made a legal entry, you can file the I-485 application for permanent residency and the I-765 application for work authorization. Because you are the spouse of a US citizen, there is no visa number quota and therefore its just a matter of processing the paperwork, which will depend a bit on your area. For instance, here in Jacksonville FL, it typically takes 6-8 months to get to an interview, but I understand that in other parts of the country it can take longer.
IF you made an illegal entry, then s/he can only file the I-130. You can't file the I-485 or the I-765, so you can't get the green card, work authorization or driver's license.
Have you applied for your green card yet? Have you discussed your eligibilty (i.e., previous immigration and criminal history) with an immigration attorney to discuss your eligibility? In general, if you entered the US legally, your spouse will be able to sponsor you for your green card. You will receive work authorization within 90 days, and generally, the green card application takes about 6-8 months. You should seek the counsel of an immigration attorney to determine your eligibility to file the application.
Note: The content of this reply does not constitute legal advice or create an Attorney/Client relationship in the absence of an agreement for legal services/retainer with my office. This is just a place to start in deciding what to ask your lawyer.