This guide applies to Ubuntu or other Debian-like system. It should be similar on other distributions.
Google provides the Linux version of Chrome in *.deb package. To install it, you need the root privilege. But what if you just want to try it and don't feel comfortable to install this unstable version in your system? Following these steps, you can try it with a regular user account.
Step 1: Download
As of this writing, the stable release of Google Chrome is not available yet. We can download the experimental version from the development channel. The URL is:
Look for the Linux section and download the package suitable for your system.
Step 2: Unpack
Create a directory where you want to put the unpacked Google Chrome. E.g.
Extract the Google Chrome package to that directory.
dpkg -x google-chrome-unstable_current_i386.deb ~/chrome
Step 3: Run
Now you are ready to run it.
The current Google Chrome for Linux is not stable yet, so you don't want to use it for serious e-business.