The deadsnakes PPA make the latest stable versions of python available on LTS distributions. I now find it preferable to installing from source, whether from download or using pyenv.
The following was tested on a stock Ubuntu 18.04.3 LTS desktop with python 2.7.15 and 3.68 as the shipping system python versions. The pip3 binary was install using the stock python3-pip package, updated with pip3 install --upgrade pip.
One of the key reasons this works for me is that I've been aggressive about individually virtualizing project environments with venv.
First, add the deadsnakes PPA to apt:
$ sudo add-apt-repository ppa:deadsnakes/ppa
Next, do the usual update and upgrade:
$ sudo apt update -y && sudo apt upgrade
Then install the basic python3.8 packages:
$ sudo apt install python3.8 python3.8-dev python3.8-venv
This will install the python3.8 binary to /usr/local/bin.
Fire it up to verify the install:
$ python3.8
Python 3.8.0 (default, Oct 14 2019, 21:29:03)
[GCC 7.4.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> quit()
Finally, make sure you can create a virtual environment:
$ cd testing
$ python3.8 -m venv venv
$ source venv/bin/activate
(venv) $ python --version
Python 3.8.0
(venv) $