I am making my first clip and I need help with Premiere Pro.
The size of the whole project is 720 x 576.
The size of my clip into this project is 320 x 240.
When exporting, I have big black spaces around my clip.
How can I remove them?
Thanks in advance.

Click on the clip in the timeline, the in the effect controls window, under motion, increase the scale until the clip fills up the screen.

but the quality of this clip would be very low this way...

There is no way to increase the size of a clip without scaling it up and losing quality, but surely you know that? Maybe we're confused as to what you want to do...

I don`t want to increase the size of the clip!
I want to decrease the size of black fields around the image. I just want to have a 320x240 clip without black spaces around it.

Oh! Simple. Make a smaller project file or sequence or whatever they call it in premeire, and put the clip into it instead of the full-size one.

Thanks!
I`ve already managed to do it.
The next question:
Which codec to use?

Use Indeo Video 5.10 It always works for me... or you could just save it as a DV AVI which can be lossless which will bring the best quality at a very high memory size... yet If you can deal with WMVs use adobe premiere's own converter and you'll get really crisp results at really low file sizes.
I'd stay away from cinepak unless everything else turns out ugly, i hope this helps!

Thanks a lot!
I`ve used cineoack and found out that it`s a complete crap.