September 13th is the date that is already set to start pre-orders of iPhone 5C. But Apple has not yet confirm any specific time. However, two of the US carriers, Verizon and Sprint, have indicated on their sites that they will start taking pre-orders tonight when Friday, September 13th begins. It means that on midnight today i.e. at 12:01 AM Pacific Time or 3:01 AM Eastern Time or 2:00 AM Central Time, iPhone 5C pre-orders will start. iPhone 5S pre-orders will not start though Verizon do not mention it. But Apple has already told that iPhone 5S pre-orders will start with its launch on September 20th. Hence, Verizon must follow it. Sprint, on the other hand, clearly mentions that it will take only iPhone 5C pre-orders tonight.
MacRumors states that "Why Verizon?" is the tab present on its official website page for iPhone that reveals pre-order details. Verizon Wireless asks customers to sign up for getting email updates about the availability of the two new iPhones. It states, "Sign up to be reminded when iPhone 5c and iPhone 5s are available for purchase on Verizon. Pre-order begins online September 13 at 3:01 AM EST."
Sprint also states on its website that customers can pre-order iPhone 5C on 2:00 AM Central Time. iPhone 5C will also be available in for pre-order Friday midnight in 10 other countries along US. UK, Hong Kong, Australia, Canada, China, France, Germany, Japan, Puerto Rico and Singapore.
Timings to start iPhone 5C pre-orders is almost same for all countries. Just convert the announced Pacific Time into your own time zone before searching on Verizon and Sprint. Other local operators in each country can have their own time to start pre-orders. So search for their timings to buy via your local provider.
See also the Apple Store.