Experience is obviously different for each person.
It only took ten days for my Trap17 site to be listed on Google, where I used the Add URL on the Google site. In the seven days since being listed, there has been 53 hits from the Googlebot with only 10 by Inktomi Slurp and one by MSN.

As mentioned above, it really is dependant of what type of content you have and having links to your website (eg. in forums) definately helps. Indexing will not hapen overnight, but it will happen...

You can submit your website to Yahoo here -http://submit.search.yahoo.com/free/request
You have to be a Yahoo ID for siging in before submitting your website.

Hi,
I have some good news. Finally google indexed me :-). Thanks again for your recommendations in the last days. But in order to keep you active i have a new question for you:

My site is about Web Design. I would like to know in what position do i appear if you search in Google "Web Design". I mean there are a lot of pages that matched this search and i do not want to check one hundred pages. Maybe there is a function that gives you the exact position for a search.

Any idea???

Yahoo crawls my site more often than any other search sites, here are some stats from my cPanel.

Please note that Inktomi Slurp is Yahoo. Also here are the stats of how are people connected to my site.

As you can see the more people use Yahoo to search my site, the more frenquently Yahoo crawls my site.

Okay, so I found the thing in my reports that says that the googlebot found my site on May 14th, so now does that mean I just have to wait until it gets listed in google? Or should that have been done automatically? I've checked google for my site and it isn't there yet. I also submitted my link to google today (before I knew how to check if the googlebot found my site) but I don't know if that'll make a difference.

I dunno about exact position but you can measure your PageRank with sites like this and then compare it to others also offering web design services.
Also, if you've submitted your site and think you should be indexed, maybe check Google's webmaster guidelines to make sure you're not breaching any of the rules that might get you blacklisted.
You can also reduce the gap between indexing of your site with these meta tags:

Interesting. I had a much more difficult time getting listed in Yahoo then I did in Google. I submitted my site to Google, and it got listed. But getting listed in yahoo took me years! I think the problem with Yahoo was that I did not own my own domain then. Although, that is only a guess.

Sunkist