I've done this more times than I care to remember lately so I'm going to remember it here.
Boot up an AWS Ubuntu Server 14.04 instance, use MobaXterm to log in with ubuntu as the username then:
sudo apt-get update
Don't worry about grub - it's not used as far as I'm aware
sudo apt-get upgrade
Install LAMP (don't forget a password for root on MySQL)
sudo apt-get install lamp-server^
The web-root directory is /var/www/html so we'll give ourselves permission to play there using (adapted from Ulyssesonline):
sudo chgrp www-data /var/www/html
sudo chmod 775 /var/www/html
sudo chmod g+s /var/www/html
sudo usermod -a -G www-data ubuntu
sudo chown ubuntu /var/www/html/
We'll also need curl:
sudo apt-get install php5-curl
and Mcrypt:
sudo apt-get install php5-mcrypt
sudo php5enmod mcrypt
sudo service apache2 reload
Sort out Mod-rewrite
sudo a2enmod rewrite
sudo service apache2 restart
Move to web-root
cd /var/www/html/
Next to figure out how to install Laravel.