If you find yourself maxing out your free amounts of storage and would like a little more control about who can see what's in your cloud then you could do no worse than following some of these recommendations.
Get Yourself Some Storage
The first thing you'll need to roll your own cloud is some storage. This may be a NAS drive, or server running a version of Linux or at the very least a USB HDD. Depending on what you have on this storage and how important it is should determine what you do about backing it up. I'd strongly recommend using a RAID of disks do that if one fails the mirror can pick up the slack.
If you are going down the NAS route make sure you pick a device that can share folders using the WebDav protocol. WedDav is widely used protocol which allows tablets and computers to browse a folder structure over the Internet.
If you are running a server then again make sure that you are running WebDav on it as this will be your primary means of connecting to the data store.
If you have a USB HDD then you probably have the most work to do as you will need a device that will act as a server. I'll be looking at Raspberry Pi in the future to carry out this task. Full instructions can be found here: http://petrockblog.wordpress.com/2012/08/15/your-own-cloud-server-with-owncloud-on-the-raspberry-pi/
Set up Dynamic DNS
Follow this tutorial to get yourself a free Dynamic DNS account from DLink. You will then have a URL that you can use to route to your Internet connected device.
You will also need to forward the WebDav ports 80 and 443 to your devices IP address on your home network. You will need to search the Internet for a guide on how to do this for your particular router and there are too many variations for me to cover here.
Last but not least you need some software that can connect to your cloud. Documents from Readdle is brilliant if you have an iOS device. There are free and paid WebDav clients for Android which will get you going or OSX and Windows natively support the protocol.
By now you should start to find it relatively easy to connect to your files whilst away from home. However if you are getting stuck then please let me know as I will point you in the right direction if I can.