It's a fairly simple operation but I struggled to find much on the internet to assist prior to starting so have written this to help others.
New batteries are available from ebay, search for "Tom Tom One V3 Battery" and you should find loads. Expect to pay about £8-£10 delivered.
You will also need a Torx 8 or T8 driver to remove the screws. These are available in the UK from Maplins, B&Q and Screwfix, often in a combined security driver pack.
Before you start:
Remove any SD cards
Backup the TomTom using the TomTom suite software supplied with the unit. You shouldn't affect any data on the unit but best be safe!
Step 1: Remove screws and open case
Once removed use your finger nails or an old credit card to open the case at the top, it splits between the silver and grey section as shown. Once as shown the grey back section slider down off the unit to clear the SD card and USB port.