The google directory is from the Dmoz rdf dump so you need your site submitting to http*://dmoz.org, read the submission rules very carefully and get all your details absolutely spot on other wise you will not be accepted.
The only way you can see if your site has been accepted is to either check the category you choose for your submission or to search for it from the home page, be prepared for a long wait, these editors are volunteers and there has been times when you have to wait for months and months.
Don't keep submitting otherwise your site will never get accepted, leave it a few months in between and make sure you submit to the same category each time otherwise it will look like you are trying to get your site into multiple categories
They do have a forum which you can request details of where you site is in the queue but we can't post the url due to the TOS of this forum
Yahoo is by paid submission, also read the submission rules carefully even though you may be rejected at least with yahoo they give you a chance to correct any errors you may of made with your submission.
Other web directories also use editors to check site submissions so make sure you read the submission details of each individual directory before submitting as each one may have different guidelines for you to follow
With other search engines just click on the "submit your url" or "submit your site" link (whatever they use for wording) and complete your sites details, its that simple it just takes time going to each one, under no circumstances use any automated submission software unless you know what you are doing or this could have an adverse effect for your site by getting it banned.