Computer backup batteries are typically easy to replace, and usually pretty easy to find. Most of the lead acid batteries are commonly used inside the battery backups, and are usually easy to replace. This is why my current choice for battery backup units is APC, they are just plug and play, and their support is great. As you can see from the picture below, replacing this battery is a piece of cake.
APC Backup Battery
TIP! Most battery backup units will warn you when it is time to replace the battery with either a warning light, or an audible beep. Check the manual or the manufacturer's website if you're not sure when you need to replace the battery.
Some batteries are very easily replaceable, while others will require some work and tools. It is usually very easy to check. The online documentation and support available from the manufacturer of your backup will let you know if it's something you can tackle.
There are many different suppliers on the internet that you can get a replacement battery for your backup. Finding a trusted source that is in the same country you live is recommended. Because of the chemical nature of the battery, if you buy from a different country, your shipment might get held up at customs, or confiscated.
Now that I've told you where not to buy your backup battery, where can you buy it. For USA and Canada, go to Tigerdirect.com first, if they don't have what you're looking for, try Ebatts.com. If you can't get one in the same country that you live, talk to your local customs before you order to make sure you get your battery.
When your new battery arrives and you're ready to install it, make sure you turn off the power on all the devices plugged into the power supply unit. Then turn the unit off, and lastly, remove the power plug from the wall. This way, the power unit can not try to intervene and use the battery at the same time you're removing it.