Nothing is obvious from your post.
It is not clear from the limited info that you have given what you have done
You appear to have downloaded the update version which will not work if you don't have 10.8 installed. As you have purchased 10.8.3 from App Store, click on download again. As far as I am aware 10.8.3 is the version that will be downloaded for all people who buy from App Store.
the situation is that: I have purchased os x 10.8.3 from the app store and downloaded it. I downloaded it the second time also and tried to say install. It didn't go, as it says that this update can only be installed if I had 10.8 version. I tried to find a 10.8 version in the apple store but it doesn' exist. they only give 10.8.1 and I downloaded that either. I wasn' asked to pay for it. But I could not install it. also the version 10.8.1 demands os x 10.8 to run.
So my question is how do I get the version 10.8 on my system?
Rebeka, the only version of Mountain Lion available in the Mac App Store is the full 10.8.3, there is no 10.8 that it builds on. If you purchased ML for $20 and you downloaded, you should be able to install by clicking on the file name (should be in your Applications folder) and then follow the on-screen quetions and answers to accept and agrree, etc. and then install.
You should have a machine that meets the ML specs or it should not have allowed the download: http://www.apple.com/osx/specs
What is the name of the file and when you click on the installer, what do you see next on the screen?
I have the file OSXUpd10.8.3.pkg, that I paid about 20 euro
i double click it and I get a window named Install OS X Update, quickly after a rollover this window saying:
This update requires OS X version 10.8
and a button named: Close.
I can only click that button and everything closes up...
am I helpless....?
Ok, the problem is somehow you have managed (not blaming or anything like that) to download the update pakage and not the full Mac OS X version. Your file is probably only about 300-400 MB when unpacked and the full installer is about 4-5 GB.
Reopen App Store, then on Purchases, hold down the Option key when you click Purchases. That should show you the entire purchase list, including your recent attempt at ML download. You want a file like Mountain Lion, and not Mountain Lion Update. See what titles are shown when you do an Option-click on Purchases.
The task at hand is to download the correct file, the problem is finding it first. For some reason the system has given you the wrong file.