Use a version of pip installed against the Python instance you want to install new packages to.
In many distributions, there may be separate python2.6-pip and python2.7-pip packages, invoked with binary names such as pip-2.6 and pip-2.7. If pip is not packaged in your distribution for the desired target, you might look for a setuptools or easyinstall package, or use virtualenv (which will always include pip in a generated environment).
pip's website includes installation instructions, if you can't find anything within your distribution.
Update: In the modern (2020s) world, python -m pip is the right way to do this, where python can be replaced with whichever interpreter you choose.