I have a PC with a pentium celeron 1.2GHz, 256MB of RAM and 40 GB HDD space . I have a dual boot system with:
1. Windows XP pro SP1 &
2. Ubuntu 7.04
XP is working perfect but ubuntu is very very slow!!! Which would be the best linux distribution for this configuration. I want to make linux as the OS for my PC and the best one fast! Please help me!!!!

I run Debian on a similar machine and it works fine. you could also install XFCE as the desktop instead of gnome, which would help improve the speed.

Debian XFCE install CD1

Debian Netinstall CD you could install from the netinstall CD, then once complete install XFCE and then when you login to the box you could choose the desktop environment you want. (gnome or xfce)

If you already have Ubuntu installed, you can install XFCE with:
sudo apt-get install xubuntu-desktop

This will get you Ubuntu with a complete xfce desktop. Which means more lightweight programs and a lightweight Desktop Enviroment, but it's still Ubuntu, just with different Programs pre-installed.

Since you only have 40 gigs, you will want to uninstall the unnecessary Ubuntu packages - see this:
http://www.psychocats.net/ubuntu/purexfce

If certain programs are still too slow, simply replace them with more lightweight ones. For example Dillo as Webbrowser. Look at what is packaged into distributions like DSL and Puppy Linux. I do not recommend to install them. They are meant as live cd's, and that's what they do best. But they have a lot of programs that will run great on older hardware, and you can install them through synaptic in Ubuntu.

The only thing that is holding this computer back is the 256mb ram, which is the bare minimum for pretty much all modern operating systems - including windows xp. You will notice a huge improvement if you just get another 256mb ram.