Debian

Codename	Version	Released	LTS Until
buster	Debian 10.0	July 6th, 2019	2024
stretch	Debian 9.0	June 17th, 2017	June 2022
jessie	Debian 8.0	April 26th, 2015	June 30th, 2020
wheezy	Debian 7.0	May 4th, 2013	May 31st, 2018
squeeze	Debian 6.0	February 6th, 2011	February 29th, 2016
lenny	Debian 5.0	March 10th, 2012
etch	Debian 4.0	May 22nd, 2010
sarge	Debian 3.1	June 6th, 2005
woody	Debian 3.0	July 19th, 2002
potato	Debian 2.2	August 14th, 2000
slink	Debian 2.1
hamm	Debian 2.0
bo	Debian 1.3
rex	Debian 1.2
buzz	Debian 1.1

APT

On your current version, make sure everything is up to date.

apt-get update
apt-get upgrade
apt-get dist-upgrade

Then jump into your sources.list and change to the codename for the targeted version.

sed -i 's/wheezy/jessie/g' /etc/apt/sources.list

apt-get update
apt-get upgrade
apt-get dist-upgrade

When support runs out, change to this to keep having access to packages (just remember, it's an archive!)

deb http://archive.debian.org/debian wheezy main contrib non-free
deb-src http://archive.debian.org/debian wheezy main contrib non-free