If you did not change the default set of packages when using the python.org installer, typing python from a command line should run the newly-installed Python 2.7.  (You will need to start a new terminal session after running the installer to see this.)  The current python.org installers for OS X create a folder in your Applications directory named Python m.n depending on the Python version.  If you look in /Applications/Python 2.7, you'll see a file called Update Shell Profile.command.  It's a shell script; you can inspect it in an editor or with Quicklook.  Its purpose is to modify the startup files for the most common shell programs on OS X (bash, sh, csh) to ensure that the directory where the new Python's executable commands are located gets added to the front of the list of directories in the PATH environment variable, so that the python commands in it will be found before the Apple-suppled python commands are found.  By default, the installer runs the Update Shell Profile.command for you automatically.  This should result in something like this:
$ cat ~/.bash_profile
# .bash_profile
# ... other stuff
# Setting PATH for Python 2.7
# The orginal version is saved in .bash_profile.pysave
PATH="/Library/Frameworks/Python.framework/Versions/2.7/bin:${PATH}"
export PATH
If you take a look in that directory, you should see something like this:
$ ls -l /Library/Frameworks/Python.framework/Versions/2.7/bin
total 272
lrwxr-xr-x  1 root  admin      8 Nov 30 00:49 2to3@ -> 2to3-2.7
-rwxrwxr-x  1 root  admin    140 Nov 30 00:30 2to3-2.7*
lrwxr-xr-x  1 root  admin      7 Nov 30 00:49 idle@ -> idle2.7
-rwxrwxr-x  1 root  admin    138 Nov 30 00:30 idle2.7*
lrwxr-xr-x  1 root  admin      8 Nov 30 00:49 pydoc@ -> pydoc2.7
-rwxrwxr-x  1 root  admin    123 Nov 30 00:30 pydoc2.7*
lrwxr-xr-x  1 root  admin      9 Nov 30 00:49 python@ -> python2.7
lrwxr-xr-x  1 root  admin     16 Nov 30 00:49 python-config@ -> python2.7-config
-rwxrwxr-x  1 root  admin  33764 Nov 30 00:31 python2.7*
-rwxrwxr-x  1 root  admin   1663 Nov 30 00:31 python2.7-config*
lrwxr-xr-x  1 root  admin     10 Nov 30 00:49 pythonw@ -> pythonw2.7
-rwxrwxr-x  1 root  admin  33764 Nov 30 00:31 pythonw2.7*
lrwxr-xr-x  1 root  admin     11 Nov 30 00:49 smtpd.py@ -> smtpd2.7.py
-rwxrwxr-x  1 root  admin  18586 Nov 30 00:30 smtpd2.7.py*
The new python is available as the command python2.7 but there is also a symbolic link to it as python.  Because the PATH environment has been changed:
$ echo $PATH
/Library/Frameworks/Python.framework/Versions/2.7/bin:/usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin
when you type python as a command in the shell, that symlink will be found first before the Apple-supplied python in /usr/bin one of the directories where system-supplied user commands are installed (as on OS X 10.6):
$ ls /usr/bin/py*
/usr/bin/pydoc*            /usr/bin/python-config*    /usr/bin/python2.6-config@
/usr/bin/pydoc2.5@         /usr/bin/python2.5@        /usr/bin/pythonw*
/usr/bin/pydoc2.6@         /usr/bin/python2.5-config@ /usr/bin/pythonw2.5@
/usr/bin/python*           /usr/bin/python2.6@        /usr/bin/pythonw2.6@
(Note, in general, you should not attempt to modify or delete files in /usr/bin since they are part of OS X and managed by Apple.)
There are many ways to manage multiple Python installations on OS X; check the archives or the web.  One thing to keep in mind is that you can always use an absolute path to the desired python command to check.  So with the modified path as above you should see the following behaviors:
$ /Library/Frameworks/Python.framework/Versions/2.7/bin/python2.7 -c 'import sys;print(sys.version)'
2.7.1 (r271:86882M, Nov 30 2010, 09:39:13) 
[GCC 4.0.1 (Apple Inc. build 5494)]
$ python2.7 -c 'import sys;print(sys.version)'
2.7.1 (r271:86882M, Nov 30 2010, 09:39:13) 
[GCC 4.0.1 (Apple Inc. build 5494)]
$ python -c 'import sys;print(sys.version)'
2.7.1 (r271:86882M, Nov 30 2010, 09:39:13) 
[GCC 4.0.1 (Apple Inc. build 5494)]
$ /usr/bin/python -c 'import sys;print(sys.version)'
2.6.1 (r261:67515, Jun 24 2010, 21:47:49) 
[GCC 4.2.1 (Apple Inc. build 5646)]
$ /usr/bin/python2.6 -c 'import sys;print(sys.version)'
2.6.1 (r261:67515, Jun 24 2010, 21:47:49) 
[GCC 4.2.1 (Apple Inc. build 5646)]