OK OK. There are 3 categories of mining. Mining speed is measured in Megahashes/second (or kilo, obviously)
GPU Mining - Very fast, makes me around 700Mhash/s with two video cards. You need graphics cards (preferably AMD) to make this work. You also need to download a client.
CPU Mining - Mining using your computer and a mining client. This is not profitable, you are likely losing more in power cost than you put in.
Web Based Mining - A newish type of CPU mining which uses Java or Javascript. Really easy for newbies to use, but comparitively incredibly slow.
In short, mining is only profitable using graphics cards (not regular processors) and you've so far been using the slowest form of mining. Laptops do not have the GPUs available for such tasks, so unless your power bill is paid by someone else it is more profitable to turn the computer off unfortunately!
The Bitcoin client itself is what you need to use to get paid your reward from the site or mining pool you were using. It's fairly easy to use, but people on this forum will help you if you have more specific questions about how it works (though you are better off not asking in the mining forum, as that is purely for stuff about mining coins and not just usiong bitcoin
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