I am a graduate student currently on an F1 visa and will have an H1B visa from October onwards. I graduated December 07 and worked on a contract position from 18th April 09 to 11th September 09. The company pays me an hourly rate and does not deduct taxes from my payment.

I will move 14th September onwards to another company on a full time position with an pre decided annual salary and biweekly pay and tax deductions.

How should I go about filing my taxes especially for the months I was on my OPT on F1 visa? Should I be paying medicare and social security taxes for this period too?

Thanks,

If you are not married, then for 2009 you will file nonresident tax return with Form 8843.
You have OPT income as independent contractor, which you will report on schedule C or C-EZ (form 1040). In your case, this income is not subject to SE tax.
Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents (http://taxipay.blogspot.com/2008/03/us-tax-filing-requirements-for-non.html)

Note that SE (self-employment) tax is the equivalent of FICA (Social Security and Medicare) taxes, which the self-employed pay under Schedule SE.

Because you are exempt from FICA (Social Security and Medicare) taxes, you are also exempt from SE taxes.