I will show the steps using Python2.7.13 If you download a newer version it should work similarly.
cd ~
wget https://www.python.org/ftp/python/2.7.13/Python-2.7.13.tgz
tar -xzvf Python-2.7.13.tgz
cd Python-2.7.13
./configure --prefix=~
make altinstall
The configure and make step takes few minutes. Now python 2.7 would be present in ~/.local/bin
Add this to PATH
export PATH=~/.local/bin:$PATH
python2.7 # should work fine
It is a good idea to add the export statement to ~/.bashrc file to load at login.
You can also create a soft-link to python2.7 so that python command gives you 2.7
cd ~/.local/bin; ln -s python2.7 python
Lets talk about installing pip.
Download the get-pip.py file and install it for the current user.
It will leave pip and pip2.7 executables in ~/.local/bin.
cd ~
wget https://bootstrap.pypa.io/get-pip.py
~/.local/bin/python2.7 get-pip.py --user
Pip shows some ssl warnings. You can fix those by doing the folowing.