I lived in Ashgabat from 2012 to 2013. I did not marry which was a big mistake in my life. But for your answer, what I knew at that time was a condition that one should have lived in Turkmenistan at least for one year and must have, his or her, own house or flat in Turkmenistan. Some other formalities like your passports, documents and some government fees. It may take three months to get your marriage certificate after which you can marry. The day of marriage is fixed in Turkmenistan, looks strange but its their way. To witness your marriage, a government representative is present in the function.