For simply accessing the data on your Xperia (including the microSD card) for transfer to/from your computer, the required driver is included with Windows and should be installed automatically by Windows the first time you connect your phone to it.
If that doesn't happen on Windows XP, it's probably because you don't have the required Windows XP Service Pack installed.
I believe you need at least Service Pack 2 (SP2), but best to install Service Pack 3 (SP3) as that's the final update pack for XP.
You can get SP3 via Windows Update, or you can install it yourself by downloading the network installation package from here:
http://www.microsoft.com/en-gb/download/details.aspx?id=24
For performing more advanced operations with the Xperia on your computer (eg backup & restore) you need to install the Sony PC Companion software which definitely requires SP3 on Windows XP:
http://www.sonymobile.com/gb/tools/pc-companion/