From Wiki

First you need to find out where your local office is located, see the attached link http://www.ssa.gov/reach.htm#office

you will need to complete the attached form

http://www.ssa.gov/online/ss-5.pdf

After 2 weeks of being admitted with the appropriate immigration category (employment authorized) you will need to go to the local office yourself with the completed form and your passport with the visa stamped in it together with the I-94 form stamped by immigration officer when you entered the country. This can also be done after receiving an EAD/Employment Authorization Document or Green Card/Permanent Resident card. Allow a couple of weeks for your status to be updated.

Do not try and visit the office the day or the week after you arrive in the US it takes the different agencies time to transfer information between each other. Within 2 weeks you should receive in the mail your card with your unique SSN.

Note: If you are on H4 visa, you are NOT eligible for a SSN, but you are eligible for a Tax Identification Number. Your spouse should apply for this with his/her next tax return, although you can apply for it throughout the year.

http://www.irs.gov/individuals/article/0,,id=96287,00.html