Where do I record the sale of a website business with no physical assets?

Since this was a business, you will need to report this as business income in Turbo Tax. please follow these steps.

Log into your Turbo Tax return and do the following:

1) Select the federal tab in the left navigational screen in your return

2) Select wages and income at the top of the screen and then select add more income

3) Select Self-employment and then select show more

4) Select Self-employment income and expenses and then select start

5) Just follow the interview and answer the questions as they are asked. You will need to complete the profile section of your business 

6) After this is complete it will ask for income information.  If you have a 1099 MISC form, you will need to enter the form.  If you don't have one, then you can enter your income as other common income.

7) After this is complete, the program will try to find deductions unique to your work. After the program finishes doing this, you can now enter expenses for your business.

If you are in your first year of business and have no income, don't panic. IRS does recognize that there may not be any income in your first year of business.  The IRS will expect you to make a profit in the future or else they might reclassify your business as a hobby. Here is a link to select to find out more on how IRS may make this determination.