How to get on the search engines

I built a website, and I want to know how the correct way to get it recognized by the search engines. My understanding was there "was" or "is" crawlers that used to search for meta-tags. But then I read that the search engines do not do that any more and meta-tags are of no use.

I've gone to google and typed in my website name, and I used to get only two entries...none of them to my webiste... just to some guy in yugolsavia, who lists all registered domain names...lol...

But now I type in the name and a gazzillion answers come up, and none of them my website...

So, please explain if meta-tags are still useful and how I get on the search engines, without paying some third party person a bunch of bucks  to register me for their profit...