You submit your URL, then wait from 4 to 6 weeks to see if the engine has listed it (there is never any guarantee that the engine will index your other pages), except in google you can verify your website by signing into google and going into webmaster tools.
Just because your URL is submitted, doesn't mean that people will find your website just with the keywords listed on it!
(Header tags are important... You know, the <h1> and <h2> and <h3>, that somehow happen to contain 1 or 2 of your keywords)
Some search engines have different versions, as in, for different languages - You must submit to them individually
There are 2 ways to submit
1. Manually - which gives you the ability to verify your submission (higher percentage of getting listed)
2. Automatically - no guarantee with the top 3 search engines, but you may get listed on the rest (and there are over 100)
I wouldn't recommend automatic to anyone... Well, almost anyone, as there are some websites that are quite sick