This will be my first time filing taxes under 1099 form. I wanted to know what can I claim and what I can't claim for 1099 form ?

The Form 1099 only reports the income earned.

You report your income (as stated on Form 1099) and you expenses on Schedule C.

Whole books have been written detailing what you can and cannot claim on the Schedule C, so it is impossible to detail on this forum, especially since I have no idea the nature of your work.

If it is 1099-misc, then you have income as independent contractor.
You are self employed or independent contractor. You will report your income and expenses on schedule C or C-EZ (Form 1040). This income is subject to SE tax at 15.3%. Read: Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor (http://taxipay.blogspot.com/2008/04/tax-filing-by-self-employed-sole.html)