Well, upgrading the Hard Disk Disk Drive capacity can be done in different options:
1) Replacing your Hard Disk Drive to a bigger storage capacity 250GB~max available), but you need to back-up or save your files in order to transfer them to the new one.
2) Some units have the expandable features, where you can add Hard Disk Drive without removing the existing one. Usually you can see an extra slot in the casing for additional drives.
3) Buying External Disk Drive with even much bigger capacity, and not having to remove your exisiting files.
It will then depend to your preference, but if I am to choose, I'd opt for the External Disk Drive, since it would also offer great flexibility and hassle in installation coz it's just a plug and play function. But then, if you prefer to replace the existing to a new one, you need to follow carefully the installation steps provided by the brand's customer support. Example, for HP Pavilion a1010n Desktop PC, the steps are clearly provided in this link : HP Pavilion a1010n or download the .pdf file at this link: HP Pavilion a1010n HDD Upgrade.