The part about "just don't worry about it" is not really great advice, IMO. I think the rest is good, particularly the part about using tax software and/or doing a Schedule C. Just do what it says - it's pretty simple for small businesses - the amount in taxes paid will be fairly minimal. If you use tax software, use the business version and answer the questions and it'll figure it all out for you basically (might even find some deductions if you had expenses, like domain names, hosting, etc.).

While the IRS likely won't audit you for a few hundred dollars (US), there are laws about what you have to do. You don't need to become a tax expert, but knowing the very basics so you don't run afoul of any laws and end up owing some $$ or penalties is probably worth taking a bit of time to do at the end of the year.