Mysql 5.6

Debian 7

apt-get install libaio1
wget "http://cdn.mysql.com/Downloads/MySQL-5.6/mysql-server_5.6.21-1debian7_amd64.deb-bundle.tar"
tar xf mysql-server_5.6*-1debian7_amd64.deb-bundle.tar 
dpkg -i mysql-*.deb

Debian 6

cd /usr/src
wget http://www.mysql.com/get/Downloads/MySQL-5.6/mysql-5.6.20-debian6.0-x86_64.deb/from/http://cdn.mysql.com/ -O mysql-5.6.20-debian6.0-x86_64.deb
dpkg -i mysql-5.6.20-debian6.0-x86_64.deb
rm mysql-5.6.20-debian6.0-x86_64.deb
mv /etc/mysql/my.cnf /etc/my.cnf
cp /opt/mysql/server-5.6/support-files/mysql.server /etc/init.d/mysql.server && update-rc.d mysql.server defaults
apt-get install libaio1
chown -R mysql /opt/mysql/server-5.6/
chgrp -R mysql /opt/mysql/server-5.6/

upgrade mysql

/opt/mysql/server-5.6/scripts/mysql_install_db --user=mysql --datadir=/var/lib/mysql
rm /opt/mysql/server-5.6/my.cnf 

vi /etc/my.cnf
basedir = /opt/mysql/server-5.6
lc-messages-dir = /opt/mysql/server-5.6/share
remove language = …

Centos 6

yum install libaio perl
yum remove mysql-server mysql

wget --content-disposition http://dev.mysql.com/get/Downloads/MySQL-5.6/MySQL-shared-compat-5.6.20-1.el6.x86_64.rpm/from/http://cdn.mysql.com/
wget --content-disposition http://dev.mysql.com/get/Downloads/MySQL-5.6/MySQL-shared-5.6.20-1.el6.x86_64.rpm/from/http://cdn.mysql.com/
wget --content-disposition http://dev.mysql.com/get/Downloads/MySQL-5.6/MySQL-client-5.6.20-1.el6.x86_64.rpm/from/http://cdn.mysql.com/
wget --content-disposition http://dev.mysql.com/get/Downloads/MySQL-5.6/MySQL-server-5.6.20-1.el6.x86_64.rpm/from/http://cdn.mysql.com/

rpm -ihv MySQL-shared-compat-5.6.20-1.el6.x86_64.rpm
rpm -ihv MySQL-shared-5.6.20-1.el6.x86_64.rpm
rpm -ihv --force MySQL-server-5.6.20-1.el6.x86_64.rpm 
rpm -ihv --force MySQL-client-5.6.20-1.el6.x86_64.rpm

/etc/init.d/mysql restart
mysql_upgrade

Centos 5

Remove old mysql server and install packages needed for upgrade

yum install libaio perl
yum remove mysql-server mysql

Install mysql-community repository

wget http://dev.mysql.com/get/mysql-community-release-el5-5.noarch.rpm
rpm -Uvh mysql-community-release-el5-5.noarch.rpm

Check for successfully added repository and install new mysql-server

yum repolist enabled | grep "mysql.*-community.*"
yum install mysql-community-server

Recreating/upgrading tables engine, first manualy run mysql-server and after successfully upgrade set ownership of /var/lib/mysql back to mysql

mysqld_safe --skip-grant-tables --skip-secure-auth --skip-networking
mysql_upgrade -p
chmod -R mysql:mysql /var/lib/mysql

Mysql start/check/stop service

service mysqld start
service mysqld status
service mysqld stop

how to yum ref: http://dev.mysql.com/doc/mysql-repo-excerpt/5.6/en/linux-installation-yum-repo.html