Foreign qualification
A corporation is "foreign" in every state but the one that created it, and a Delaware corporation doing business in another state generally must register there. This is called foreign qualification. The company appoints a registered agent in that state, files a short application with a Delaware certificate of good standing, pays a fee, and from then on files that state's reports and pays its taxes.

What counts as doing business
Each state defines doing business for itself, and the definitions are vague at the edges. In general a company is doing business in a state when it has an office there, employees regularly working there, property there or a continuing pattern of in-person business there. Most statutes also list activities that do not count on their own, such as holding meetings, keeping bank accounts, selling across state lines or a single isolated transaction.
For a startup the practical triggers are simple. If the founders work from an office or a home in California, the company is doing business in California. Hiring someone who works in a state, even remotely from home, usually requires payroll registration there and often foreign qualification. And a warehouse, inventory or a shop counts too.
A company that should be registered and is not can be fined, can owe back fees and taxes and, in many states, cannot sue in that state's courts until it registers. Registering late is fixable, just more expensive than registering on time. States charge a registration fee and annual or biennial report fees, and many impose minimum taxes. California, for example, requires a Statement of Information every year and charges corporations doing business there an $800 minimum franchise tax, so budget for your home state's costs alongside Delaware's.
Payroll registration
Before you pay your first employee in a state, register with that state's tax and labor agencies for withholding and unemployment insurance. Each state where an employee works generally requires its own registration, even for one remote employee. Payroll providers handle most of this, though they need the company's authorization and sometimes need the company to complete registrations directly. Employees in a state also bring that state's employment law with them: its minimum wage, overtime rules, paid leave, final paycheck timing and required notices.
Sales tax
States, and in some states cities and counties, impose sales tax on goods and on some services, and a company must collect it where it has nexus, meaning a sufficient connection to the state. Since the Supreme Court's 2018 decision in South Dakota v. Wayfair, nexus can come from sales alone, without any physical presence. Most states set a threshold, often $100,000 of sales into the state in a year, and some also count transactions. Whether software, SaaS and digital products are taxable varies widely from state to state.
Once you cross a state's threshold for taxable sales, you must register there, collect tax on future sales and file returns on the state's schedule. Collecting tax without registering and failing to collect after crossing a threshold both create liability. Corply tracks sales tax nexus for its customers and can register, collect and file where it applies.
Registering in a state usually also means filing its corporate income or franchise tax return every year, even when the company has losses, and some states charge a minimum tax regardless of income. Your accountant will apportion income among the states where you do business.