Congratulations on starting your own business! Business income is taxed whether you're a minor or not; you just probably don't have as much of a deduction if you are still going to be claimed as a dependent on your parents' return. (And you probably would be still claimed as one, unless your efforts are so successful that you start supporting yourself in a substantial way rather than them supporting you.)
How much money I have to earn before the US Government requires me to declare it as taxable income
Well, in order to determine whether you need to file a return when you're a dependent of somebody else, look at Table 2 in Publication 501. For 2018, if you're single, a dependent, not blind, and under age 65, you need to file a return if your unearned income (generally things like bank interest and other investment income) is over $1,050, or your earned income (which your own business would be) is over $12,000. (Or if the combination of them brings you over a threshold as well.)
If you have tax withheld from jobs, or in other circumstances, you might want to file a return and report it anyway, to get a refund of any taxes that were withheld but you don't actually owe.
How it is declared - should it be on a parent's tax returns or by forming an LLC, etc.
Generally earned income you'd get would be on your own tax return. There are a lot of business structures, and I think advising you on whether an LLC is the way to go or not may be a bit beyond the scope of this site (it's certainly beyond my meager understanding). But you could take a look at the IRS site on Business Structures, which tells you the options and what forms would need to be filled out for each of them.
There's a lot of Small Business information on the IRS site, really, and it'd probably be wise to take a look through it if you want to get a better handle on what's involved in taxation of business income.