How do I petition my girlfriend to USA if we are same-sex couples?

If she can come to the US on other visa, you may marry her in the US and file immigrant petition with the USCIS.  It may take about 6-8 months depending on the location to receive interview notice.

If she cannot come, you can either file fiancée visa or if you marry her you can file I-130 first, after approval she will get an immigrant visa interview in her country (US Embassy).

You should consult with an immigration lawyer for advice and possible representation.