US citizen recently married and living abroad

You can file married filing jointly or married filing separately if your spouse is a non-resident alien. If the latter and your spouse have no US source income, he/she would not be required to file. The IRS discusses the joint return election here  Note: to use the joint return the non-resident alien would be treated for tax purposes as a US resident alien. That means they would be taxed on their worldwide income, although the foreign earned income exclusion may apply.

SSN or ITIN  If your spouse is a nonresident alien and you file a joint return, your spouse must have either a Social Security Number (SSN) or an Individual Taxpayer Identification Number (ITIN). To get an SSN for your spouse, apply at a social security office or US consulate. You must complete Form SS-5. You must also provide original or certified copies of documents to verify your spouse's age, identity, and citizenship. If your spouse is not eligible to get an SSN, he/she can file Form W-7 with the IRS to apply for an ITIN. Refer to Taxpayer Identification Numbers (TIN) for more information.