By default centos comes with python 2.6. In most of the cases we might need python 2.7 or later to be installed. Below are few ways to install python 2.7 on centos 6.x.

Method 1 - Using SCL (centos 6.5 and earlier)

First off, update the system to the latest state. Just in case there are any pending fixes.

yum -y update

Next install the SCL Softwate Collection repository for centos.

yum install centos-release-SCL 
yum install python27

Setting the default for the shell.

scl enable python27 bash

This will set all the path required.

Installing pip.

wget https://bootstrap.pypa.io/get-pip.py
sudo python27 get-pip.py

Method 2 - Manual Install (For Centos version earlier than 6.5).

First off, update the system to the latest state. Just in case there are any pending fixes.

yum -y update

Install Dev Tools

yum groupinstall -y 'development tools'
yum install -y zlib-devel openssl-devel sqlite-devel bzip2-devel

Download Python, Configure, build and Install.

wget https://www.python.org/ftp/python/2.7.8/Python-2.7.8.tgz  
tar -xvzf Python-2.7.8.tgz

Configure and build python and Install.

cd Python-2.7.8
./configure --prefix=/usr/local
make

Install python.

make altinstall  

Setting path and Installing pip

#  Example: export PATH="[/path/to/installation]:$PATH"
export PATH="/usr/local/bin:$PATH"

Installing pip.

wget https://bootstrap.pypa.io/get-pip.py
sudo python27 get-pip.py

More details in the link here