How do I claim my moving expenses incurred in 2013 in my 2014 tax return? I won't be filing 2013 tax return because I didn't work in 2013 tax year. I recently moved to US and will start job from 2014. The move was related to work and thus is deductible.
According to the IRS (publication 521 that Joe mentioned in the comments):
Expenses not reimbursed. If you were not reimbursed, deduct your moving expenses in the year you paid or incurred the expenses
However, if you receive reimbursement that is included in your taxable income, you may deduct in the year you receive the reimbursement.
So if you don't get reimbursed, you deduct it on your 2013 tax forms, by filling and attaching form 3903. You will have to file a return if you want this deduction, even if you otherwise don't have to file a return.
If you don't have any taxable income, you may hit a situation called "Net Operating Loss" (NOL). I suggest talking to a licensed tax professional (EA/CPA licensed in your state) about what it is and what to do with it. Especially if you're a non-resident (filing form 1040NR).