Hi Naz. Most if not all search engines have a way for you to submit your website. My first suggestion would be Google. Google has several things that can help you besides just submitting your site to their search engine. If you do not have a Google account go to Google.com and in the upper right hand corner there should be a link to sign up. Once you get through that your account page will have a link called Webmaster Tools. You might also wish to take a look at AdSense. When you create a profile there as well please feel free to add me to your contact list. My profile on Google is called Vicsownlife.
Yahoo has some tools similar to Google though not quite as in depth. Look up Yahoo Site Explorer for information on submitting your websites to Yahoo.
MSN has one as well. Go to
www.bing.com and in the upper right hand corner click Extras and then click on Webmaster Center.
Those are just a few and many search engines allow you to submit your site for free and also have tools to help you track your sites, their performance and other useful information.
I hope this helps. Have a great day and above all else, have fun!