How do I install Python 3 on an AWS EC2 instance?

If you do a

sudo yum list | grep python3

you will see that while they don't have a "python3" package, they do have a "python34" package, or a more recent release, such as "python36". Installing it is as easy as:

sudo yum install python34 python34-pip

Here are the steps I used to manually compile and install python3 for anyone else who wants to do it as it's not super straight forward. EDIT: It's almost certainly easier to use the yum package manager (see other answers).

Note, you'll probably want to do sudo yum groupinstall 'Development Tools' before doing this otherwise pip won't install.

wget https://www.python.org/ftp/python/3.4.2/Python-3.4.2.tgz
tar zxvf Python-3.4.2.tgz
cd Python-3.4.2
sudo yum install gcc
./configure --prefix=/opt/python3
make
sudo yum install openssl-devel
sudo make install
sudo ln -s /opt/python3/bin/python3 /usr/bin/python3
python3 (should start the interpreter if it's worked (quit() to exit)

EC2 (on the Amazon Linux AMI) currently supports python3.4 and python3.5.

sudo yum install python35
sudo yum install python35-pip

As of Amazon Linux version 2017.09 python 3.6 is now available:

sudo yum install python36 python36-virtualenv python36-pip

See the Release Notes for more info and other packages