The techniques are no different than with any other set of applications in terms of functional testing, but you'll want to wrap more security/performance testing around it. Questions that are very broad, like this one, are more difficult for us to answer - did you have a more specific question in regards to online billing?
To be general, as your question is. When I have done this sort of thing in the past you need someone on the team who is a very good analyst, and some feedback/help from a person in accounting or someone very familiar with it. Hopefully, whatever specs that are around the application are very detailed, if not you are going to be in trouble when trying to work through credits/debits and so on. Honestly, its no real different than anything else in a test approach except you need to check the details in the math and output (if you have any) from the system in case it goes to customers.
But as Linda says, you need to get more into specifics if you want more.
Nothing learns better than experience.
"So as I struggle with this issue I am confronted with the reality that noting is perfect."
The way a company I was at that did it for DirectTV was to put a bunch of QA folks (enterprise integration testing) in a "war room" with a few developers, a QA lead, and a manager. Then have them go through the 300 or so enterprise tests as fast as possible. Here's when I figured a way to start scripting/automating many of the EIT scenarios using scripts and a unit test tool that they developed. I took my idea to the "tools and automation" group and they said "go for it". Sometimes it took days to finish just one of the tests and now the automation could do it in minutes. Can you say big raise?
"Imagination is more valuable than knowledge." (AE)