A foreign registration is an authorization for a corporation or LLC formed in one state to do business in another. For example, if you incorporated in New York and wanted to open an office in New Jersey, you'd register the New York corporation to do business in New Jersey. You must register a corporation or LLC in any state where it has a business presence. Having property or an employee in a jurisdiction are examples of a business presence.
However, you don't have to register in a state just by virtue of having customers or clients there. Points of sale alone typically don't constitute a business presence.
You register in another state the same way you incorporate or organize an LLC. You file an application and appoint a registered agent. You must also provide a Certificate of Good Standing confirming that your entity is current on its incorporation state reports and taxes and remains authorized to do business. Going forward, the entity files periodic reports and pays taxes in each jurisdiction in which it's registered.
"You don't have to register in a state just by virtue of having customers or clients there. Points of sale alone typically don't constitute a business presence."
You may have to use an assumed name. A company name can only be used by one entity in any state. If you formed Widgets Inc. in New York, want to register to do business in New Jersey, and someone has already created or registered an entity in Trenton under Widgets Inc., you'd have to register under an assumed name in New Jersey. Entity type doesn't matter. You'd still have to register under an assumed name even if the existing NJ company is an LLC.