Bit disappointing that people quickly jumped to the "Dropbox" and "Google" retorts, when it was obvious OP wanted to do it himself and not use someone else's service (as was very clear in the subject itself).
It's fine and dandy if you guys want to rely on another company's service, but some people prefer to do it own their own.
First and foremost, I would recommend setting up Linux. Ubuntu is very easy for noobies. I would suggest getting a Raspberry Pi as a dedicated controller (computer) for the server. Hook the external drive up to it, and then get some good software running.
SSH is a must for maintenance
FTP is also nice (proftp is the best in my experience)
mediatomb is a great UPnP service so you can stream directly to your other devices (home computers, Playstation 3, etc.)
Samba (to create a "Windows share")
There are probably dozens I am leaving out, but these alone have allowed me to have a very powerful cloud system running from home.
Have another Pi setup with XBMC and then you've got a conduit into your media collection in a powerful media player all for another $30.
It's fine and dandy if you guys want to rely on another company's service, but some people prefer to do it own their own.
First and foremost, I would recommend setting up Linux. Ubuntu is very easy for noobies. I would suggest getting a Raspberry Pi as a dedicated controller (computer) for the server. Hook the external drive up to it, and then get some good software running.
SSH is a must for maintenance
FTP is also nice (proftp is the best in my experience)
mediatomb is a great UPnP service so you can stream directly to your other devices (home computers, Playstation 3, etc.)
Samba (to create a "Windows share")
There are probably dozens I am leaving out, but these alone have allowed me to have a very powerful cloud system running from home.
Have another Pi setup with XBMC and then you've got a conduit into your media collection in a powerful media player all for another $30.
I don't know if the OP has given us enough information to adequately help him. If he has a windows PC he might just be able to just share the drive and not have to get a separate samba server. He could also just buy a NAS with these capabilities. One other good suggestion already mentioned was OwnCloud.org
Lastly, he could by a drive dock like PogoPlug or a cloud drive like WD My Cloud
