Some day I'm going to write about the boring backoffice mechanics for folks who are doing business on the Internet but do not expect to ride the startup trajectory.

In the meanwhile: LLC incorporation. You'll almost certainly pick an LLC as a solo founder because the costs are lower, the protections are roughly equivalent, and the pass-through nature of the business makes your tax planning easier. You'll make your LLC in your choice of Wyoming or Nevada. Wyoming is institutionally more privacy conscious than Nevada is, which may matter to some of you. ("Do you want your home address trivially available on the Internet?" is a question which gives some entrepreneurs pause. Not wanting that is a totally legitimate reason to incorporate in Wyoming.) Nevada is fairly cheap, has no state income tax and no prospect of attempting to retroactively impose one later on your income, and has a fairly nice portal where you can do the one thing a year they'll require you to do. (Robosign your "annual list" and then pay a few hundred bucks for the privilege of limited liability for another year.)

You do not need to have any connection to the state you incorporate in whatsoever. Full faith and credit clause of the US constitution for the win: all states can create legal entities for anyone which all other states must treat like their own legal entities and, accordingly, states compete with each other to get corporate formations (as a source of revenue and for knock-on economic purposes). Delaware has planted the flag in "We are a very predictable jurisdiction for litigating complex court matters if it comes to that; we're going to charge you for this." Wyoming picked privacy/"low fees low services." Nevada picked "We're cheap and reliably funded by sin taxes."

You will pay taxes anywhere your business has an economic nexus. For almost all of you, this will be "where you do the work that earns the money." Importantly, this is not not not not not where your customers are, where the people paying you money are, where the money actually changes hands, where your corporation is registered, or where your bank account is. If you sell $10,000 of software on the US App Store from a Nevada LLC with a bank account in London but you physically coded the app in Croatia, your sole economic nexus is Croatia. (Run this by an accountant or lawyer if you doubt me, but if they doubt me, I'll offer them 100:1 odds that I'm right.)

Not too much changes about your life after incorporating. You'll want to get a business checking account in the name of the LLC, primarily to start segregating funds for bookkeeping purposes and secondarily for maintaining the corporate veil. You'll register for accounts/leases/etc in the name of the LLC rather than in your personal capacity. You will almost invariably be asked for a personal guarantee for any debt/lease/etc until your business has millions in revenue -- this sucks, but you'll do it. You should get a credit card (doesn't have to be a "business" card) which you use exclusively for business purposes, because this assists in you doing your most important bit of tax planning, which is keeping very, very accurate books regarding business expenses.

You will almost certainly be amazed at the variety of expenses which are legitimate business expenses. There are fairly few bright lines, and navigating the gray area is one of the reasons you will hire an accountant. They will, almost certainly, categorize thousands of dollars of things you thought were personal as business expenses; this is one of their primary functions when working for small businesses. (Examples: 100% of your WSJ subscription; 40~60% of your Internet fees; 100% of your coworking space rent; some percentage of depreciation on your laptop; etc etc.)

In the US, you'll typically file a Schedule C attached to your 1040, showing the revenue of the business, expenses, and net profits. You'll pay taxes on the net profits, and also pay self-employment taxes on them (Schedule SE). Your accountant will identify a variety of tax-saving strategies for you; the most important (after "keep good books!") for most small businesses on HN will be "establish and generously fund a retirement account."