How does one go through the immigration process and marriage?

I presume that your husband is a U.S. citizen and that you already are married to each other, but if I misunderstood and you now are seeking information about becoming married, keep in mind that the marriage ceremony must be one that you both attend, and the wedding and marriage must be valid in the place where the wedding takes place. For a foreign national who entered the U.S. lawfully and with inspection, and who then becomes married to a U.S. citizen, it is possible to process an Adjustment of Status case in the U.S. so that the spouse will become a Lawful Permanent Resident (will get a "Green Card"). This is true regardless of whether the foreign national spouse may have overstayed her visa or even may have worked without authorization. It would be wise to engage an immigration attorney who, after learning all of the relevant information about you and your marriage, would be able to advise about eligibilities, options and strategies and would be able to represent you and your husband in the process.

You can simply look for an attorney online, through a newspaper, or maybe your friends can recommend somebody.