Use sudo or su or whatever to switch to root
If you want to install the remi repositories for PHP for example
wget https://dl.fedoraproject.org/pub/epel/epel-release-latest-6.noarch.rpm
wget http://rpms.remirepo.net/enterprise/remi-release-6.rpm
rpm -Uvh remi-release-6.rpm epel-release-latest-6.noarch.rpm
Now in order to update use the remi as well as the default repos, first check what repos are installed, enable them and run update. Some examples below
yum repolist
yum --enablerepo=remi update
sudo yum --enablerepo='remi-safe' --exclude R\* update
yum --enablerepo=ius update
Something a bit more sophisticated from the IUS repositories from https://support.rackspace.com/how-to/install-epel-and-additional-repositories-on-centos-and-red-hat/
Install the IUS repository.
wget https://dl.fedoraproject.org/pub/epel/epel-release-latest-6.noarch.rpm
sudo rpm -Uvh epel-release-6*.rpm
wget https://centos6.iuscommunity.org/ius-release.rpm
sudo rpm -Uvh ius-release*.rpm
sudo yum install yum-plugin-replace
Check what services need to be restarted to enable upgrade
needs-restarting
Have to reboot for kernel updates so check what kernels are avaliable
rpm -qa kernel
Check what kernel is running
uname -r
Reboot if needed
shutdown -r now