Following up on a fixed schedule gets you paid faster and keeps it from feeling personal. Use the same steps for every customer.

Before the due date

Send the invoice the day the work is done or the order ships, with the due date in the subject line.
3 days before the due date, send a short reminder: "Hi [name], a quick reminder that invoice [number] for [amount] is due on [date]. You can pay here: [link]. Thank you!"

After the due date

Day 1: friendly email. "Invoice [number] for [amount] was due yesterday. If it's already on the way, thank you. If not, here's the link to pay: [link]."
Day 7: call the customer or their accounts payable contact. Ask if anything is holding up payment and agree on a date.
Day 14: firm email confirming the agreed date and noting your late fee policy, if you have one in your agreement.
Day 30: pause new work until the account is current. Offer a payment plan if they need one.
Day 45 to 60: send a final written notice. Decide whether to use a collection agency, small claims court, or write it off.