Unfortunately search engines won't pick up new sites immediately. Often it will take a few weeks for your website to be indexed. Even then it's quite unlikely that your website will be the first one listed in the search results to start with.
Whilst you don't need to do anything it often helps to register your website with search engines. We'd also recommend looking at how can I improve my search engine ranking position.
To check if your website has been listed yet search for site:typeinyourdomain.com replacing typeinyourdomain.com with the address of your website without http:// or www. If your website has been indexed you'll see it in the search results.