When your
Flash Web Designers site is ready, you will need to submit your site to the search engines, particularly Google. You can find the Google submission page by clicking on the "About Google" link on Google, and then locating the "Submit your content to Google" link on the page that appears. However, submitting your site to Google alone is, quite frankly, a pointless endeavour. If there are no other links to your site on the web, Google will be appear most reluctant to index your site and show results that include your pages. If there are many other links to your site, you don't even have to bother to submit it to Google - it will find your site by itself.
This is where promoting your website is important. This involves many things, including the usual way people did things before the Internet: advertisements in the newspapers, word-of-mouth, etc. You might want to consider advertising on places like Yahoo! (which puts your ads on Yahoo!, AltaVista and CNN), Ask (which puts your ads on Ask, Excite, Match.com, Gifts.com, etc) or Google. As discussed in my article More Tips on Google Search Engine Results Placement, ads can be a quick way to get onto the first page of a search engine's results page.
There are also Less Obvious Ways of Promoting Your Website, which you might want to consider.
Naturally the above guide is not exhaustive. It is a distillation of some of the basic steps to getting started with your site. If you want more information, you should read the other articles on thesitewizard.com. However, the above tutorial should get you started in putting your website onto the Internet.