A pretty easy solution is offered by Google itself – Add your URL to Google. Here’s a bit’o info from the page:
Share your place on the net with us.
We add and update new sites to our index each time we crawl the web, and we invite you to submit your URL here. We do not add all submitted URLs to our index, and we cannot make any predictions or guarantees about when or if they will appear.
Please enter your full URL, including the http:// prefix. For example: http://www.google.com/. You may also add comments or keywords that describe the content of your page. These are used only for our information and do not affect how your page is indexed or used by Google.
Please note: Only the top-level page from a host is necessary; you do not need to submit each individual page. Our crawler, Googlebot, will be able to find the rest. Google updates its index on a regular basis, so updated or outdated link submissions are not necessary. Dead links will ‘fade out’ of our index on our next crawl when we update our entire index.
Read more here: http://www.google.com/addurl/?continue=/addurl
The process itself is very simple. At the page above there is a text box where you enter your site URL and a second for optional comments on your site or blog. Once the info is entered you type in the security letters from the image on the page and click “Add URL”. Your site should be crawled by Googlebots on the next run.
If for some reason you should ever need to remove your site or blog from Google click here for more information.