I came here on h4 visa on 19/12/2013 . How my spouse can gain the exemption please guide us

Regards

When did yor spouse coe to the US?

Actually, when he/she came does NOT matter.

A married couple can file jointly irrespective of where the spouse is located. He/she never has to set foot in the United States, and he/she can be on Mars for all the IRS cares.

However, the spouse's foreign income MUST be declared on the tax return, then accounted for with either the Foreign Tax Credit (Form 1116) or excluded using the Foreign Earned Income Exclusion (Form 2555).

Further, the spouse must get an Individual Tax Identification Number (ITIN) by submitting Form W-7 with the tax return, AND must sign BOTH the Form W-7 and the tax return.

The best way to submit the Form W-7 and signed tax return is at an IRS Tax Assistance Center that accepts and authenticates foreign passports. The link below lists the cities that have such TACs:

Taxpayer Assistance Center Locations Where In-Person Document Verification is Provided

Actually it would matter as the asker would be a non-resident alien and would not be able to be treated as resident alien/dual status alin based on the first year choice as the asker came in the middle of December. So they can only be treated as resident aliens of the spouse came before December 2013.
On the side: The spouse is most likely in the US, as the asker has a H4 visa so I'm assuming the spouse is on H1

I doubt that the H-1 or H-1B spouse came in mid-December, but if he did, TaxForAliens IS correct: First Year choice would NOT an option for 2013.