So I'm using this website:
http://www.howtoforge.com/ubuntu_debian_lamp_server
to setup LAMP on my Ubuntu Virtual Machine.
Here is my question though,
This will enable me to program and test through localhost. How can I set this up so anyone on the web can access my .php pages from any Internet capable device, and they will still interact with my local database, etc?
If you open port 80 in your firewall to your local machine, it should be available to the outside world via your ip address. You will need to check your router settings to figure out how to do this, but usually it's called port forwarding.
You could then use a free service like dyndns to give yourself a domain name that you can then type into your browser such as
myserver.dyndns.org
You have a couple of options...
1) Find a site that hosts LAMP and put you site up there. Many of them allow you to register a domain name and they manage the machine.
2) Do what Ben Rowe suggested, use a DNS forwarding service (Some are free, some not). Host the site on your own machine, some ISPs do not allow you to use port 80, you might need to use another port.