Google and other search engines should pick up on your website on their own without having to do anything.
But if you want to speed up the process of google and search engines such as big and yahoo indexing your new website you can go to the links provided to submit your url to search engines.
For google search you can go to this url.
https://www.google.com/webmasters/tools/submit-url
For Bing you can submit your website using this URL.
https://www.bing.com/toolbox/submit-site-url
For Yahoo search
submit.search.yahoo.com