If you want people to find your site, it is important that it is listed on the top search engines. You can implement all the search engine optimisation (SEO) you like but if you are not listed, it won’t help much.
When you set up a blog on a common platform like Blogger there are settings which allow you to turn off the search engine indexing for your blog but it is on by default, so Google will find you (and quite quickly I should add). The search engines are already quite familiar with the most common blogging platforms so it’s quite likely you won’t have to do much to get listed. Going beyond simply being known by the engines is, of course, what SEO is all about so make sure you read the posts on this site on this topic.
If you purchase a domain, on the other hand, you might be surprised at how quickly Google finds you. For the CraftCrave domain it was almost instantaneous! I think this is because Google indexes sites like ListOfDomains. But you might have to manually submit your domain to other search engines. One quick and easy way to do this is to do a search on these engines for your domain. When nothing is found, they often ask you to submit the link if you know the site definitely exists. I needed to do this on Bing for my domain. You might also want to submit your site to EntireWeb.
If you have some time on your hands, then I recommend working your way through this chart which lists the most essential search engine registration and submission services. On the other hand, if you’re time-poor (aren’t we all?!) then you can use a search engine submission service like Search Engine Commando and Web Position Gold which are not bad choices (but are not free). Be careful with free services because you may just find that your URL and email address get submitted to places you really don’t want them to be. Some options are SubmitExpress.com or FreeWebSubmission.com which is are free in return for joining their newsletter. Note that when they submit your site to other search engines, you may also be automatically signed up to their newsletters too. In the end, it really is the main search engines that matter, so focus on those to begin with.