I formed a single member LLC in 2013 for a business that I have invested capital in, but the business has not yet launched, and therefore made no profit in 2013. (This is because it is an online business and the website has taken longer than expected to build). How should I file taxes for 2013?

anyway, you stil incur losses, expensesso, you need to file Sch C to claim you rNOL as you have no earnings , no Sch SE is required; no quarterly estimated taxes required.You may use either Form 1045 or Form 1040X to claim an NOL refund.You can use Form 1045 to apply an NOL to all carryback years. You'll get a faster refund using Form 1045 ,usually within 90 days.You must file Form 1045 no later than one year after the NOL year. Assume that you have an NOL for 2013 ,the NOL year. You're a calendar year taxpayer Jan. 1 through Dec 31 ,using cash basis.You must file Form 1045 no later than Dec 31, 2014.
Do not file Form 1045 with your original Form 1040. File Form 1045 separately and attach it to a copy of Form 1040. Instead of Form 1045, you can use Form 1040X to file for a refund. If you choose to use Form 1040X, you must use a separate Form 1040X to amend each carryback year to which you apply an NOL.It takes longer to get a refund than if you use Form 1045.One advantage is, you have more time to file Form 1040X than Form 1045.You must file Form 1040X within threes years after the due date including extensions for filing Form 1040 for the NOL year. Assume that You have an NOL for 2013 ,You're a calendar year taxpayer using cash methyod.Your Form 1040 is due April 15, 2014.You carry the NOL back to 2011 ,two years prior to the NOL year 2012. You must file Form 1040X no later than April 15, 2017 ,the third year after the April 15, 2014 due date, plus extensions.