So, can someone please link/tell me... What is the correct form to notify the person? I understand I have to notify them, then give them 10 days..? Then file the lawsuit if they don't respond in that 10 days?
That's not quite correct. According to the Washington State Court system's webpage An Introduction to Small Claims Court, the form you fill out to start your case is a multipurpose form that serves both the function of actually filing your lawsuit and notifying the defendant that you did so. Be aware that even though they have a form there on that website, they tell you to contact the court directly to obtain the form you should actually use - don't download and try to submit the form on the website.
You have basically three options for starting communication with the person who owes you money. Generally the most sensible first step is (1), the one recommended by Taxagent:
(1) Just send a letter or even an email. Ask them to pay you what they owe you, and explain why they owe you that amount. Include any of your evidence that you think will help persuade them to pay. Optionally you can say in your letter that you will file in small claims court if you don't hear back from them by a certain date.
(2) Same as (1), but also include with your letter a copy of your small-claims filing paperwork that you have filled out but not yet submitted to the court. This can be a good idea if you believe the defendant is dishonorable, easily scared, and not likely to get angry in response.
(3) Go ahead and start your small claims lawsuit. Since you believe the defendant is likely to settle, this is likely not a good choice for you.