I worked for a company call 51talk last year. They are in China. I will not get a W-2 from them but they said that i need to claim my own taxes. What do i need to do?

If you are not getting a W-2 then you are not considered an employee by this company but an Independent Contractor. 

This means that you report all the income earned for this position (regardless of getting no 1099 or W-2) and then deduct all expenses related to earning that income.

The business income and expenses will go on a Sch C Business as part of your 1040 return.  You will need to TurboTax Self employed product to do the return. 

https://ttlc.intuit.com/replies/3300068