In order to show up in search engines correctly you need to make sure you follow all the current guidelines for how to properly create a website.
We have a list of guidelines we publish for jewelry businesses, but more important than our own, Google also publishes a list of guidelines for the correct ways to create a website.
When you follow these guidelines, it is said that you are Search Engine Optimizing your website.
Here's how you would use it in a sentence:
"I need to search engine optimize my website."
"I need some SEO work done on my website."
"My website is not optimized at all."
"I have to hire a Genius SEO to optimize my website."
As you can see, the Search Engine Optimization term can be used as a noun, verb or even to refer to the person you hire to do the SEO work for you.
Please note that if you build your website from scratch following Google's guidelines you won't have to optimize the site after it goes live. This is the best approach since you don't have to worry about initial optimization mistakes.
Do it right the first time and you won't need to waste time and money later fixing it. Although the initial investment might also cost a little more money, it should not cost nearly as much as fixing it later.