How can I get a green card through marriage?

Here is the deal, if you have come to the US on ESTA, I would be very careful about doing the right thing. As a resident, your spouse can file a Form I-130 on your behalf seeking visa classification as the spouse of a resident. Problem is that you cannot file an application for adjustment of status (Form I-485) at the same time. So what that means is that you cannot stay in the US while you at awaiting a decision on your applications. Rather, I would highly advise that you leave the US and wait for your spouse to become a US citizen at which time he can file for you to come back. The alternative is that you could stay in the US to wait for your spouse to become a US citizen and then file your applications. But that carries with it a huge risk that you may run into trouble, be placed in some type of removal proceedings and face deportation and removal. I would highly suggest that you find a competent and knowledgeable attorney and discuss these options. Don't leave the US unless you understand the potential consequences of departing if you have violated the terms of your stay and don't remain unless you understand the consequences of doing so. Ask questions and become informed, that is the best advice I can provide.