You are correct. You should file the I-130. See the USCIS page Bringing Spouses to Live in the United States as Permanent Residents. (Note, lower on the page, that special conditions may apply if you are a member of the US military.)
After the I-130 petition is approved, your spouse will generally apply for an immigrant visa using form DS-260. There are other steps as well, so you may want to refer to the flow chart on the State Department's page The Immigrant Visa Process.
(If you search on the internet, you will also find information on the K-3 visa, which would allow your spouse to travel to the US and then apply for adjustment of status to that of a permanent resident. Apparently, K-3 processing takes around the same amount of time as immigrant visa processing, so it is not advised to pursue that route.)
Note that the immigrant visa application isn't strictly an application for a green card (I-551). The way it works is that the immigrant gets an immigrant visa in his or her passport, which becomes a temporary I-551, valid for one year, as soon as the immigrant is lawfully admitted to the US. At that point, the immigrant is a "lawful permanent resident" of the US. The actual green card arrives in the mail some weeks later.