The easiest way to install the latest version is by using pip/easy_install to pull it from PyPI:
pip install tweepy
You may also use Git to clone the repository from Github and install it manually:
git clone https://github.com/tweepy/tweepy.git
cd tweepy
python setup.py install
Python 2.6 and 2.7, 3.3, 3.4, 3.5 & 3.6 are supported.