Hi beckies,
Thanks for posting your question. I'm more than happy to help you. You'll want to focus on Google (since they carry 60% of search traffic across the Internet) and Yahoo/Bing. Google has a few methods to let them know your website is there. The easiest way is to set up a Google Webmaster Tools account for your domain.
Google Webmaster Tools is a great tool Google provides to help you understand how they see your website. We have quite a few guides on setting up Google Webmaster tools. Here's a good link we have that may help you out:
Introduction to Webmaster Tools
Now, you can also use their tool to let them know you have a new URL you'd like to be indexed and included in the search results. Here's a link to that page:
Submit your URL to Google to Crawl
As for Bing, you can submit your website to be indexed by going to the link below:
Submit your URL to Bing to be Indexed
I hope this helps! If you need further assistance please feel free to contact us.
Thanks!
Tim S