You have 2 options, a) run an Apache web server with CGI scripts to call external commands, or b) access the Pi remotely with ssh (using ConnectBot for Android).
Before getting started your Pi must have a valid internet connection and an external IP address that doesn't change.
Next you must access your router to create a port forwarding rule to expose services require for remote access.
Since the internet is full of dirtbags trying to pwn your machine I would suggest changing your default login password, and change the port numbers for your ssh service and Apache web server to something less common.
When I was on holiday in Vietnam and Thailand last year I had my Pi running remotely for a cool 4 weeks on and off (power source controlled via a special latching circuit triggered by land line incoming call detection).
It was great fun I could do everything on my Pi despite being 6000 miles away, stuff like check my road cam / weather cam, upload files, access the BBC iPlayer (cos I was missing out my favourite sci-fi series).
I also had ssh running on my Pi this provided an encrypted proxy network layer so I can use my Android phone (via SSH Tunnel) on unsecured free Wifi without getting hacked.