I have never used MICROS specifically but I have integrated with many systems before and I generally find that if you call them and tell them you want to integrate they will usually be willing to tell you where their data is stored, also using their software for purposes other than what they intended could be copyright infringement unless you ask; also you would unofficially be a data processor for MICROS then and you don't want to get sued, so its probably best to ask.
Generally speaking though you can probably find the data you want just by performing a single action before the you open so as not to confuse matters and looking through the files in the install directory until you find information on the action you just performed, take note and repeat for each action. Then you can watch the directory for changes and if the file is one of the ones you care about then process it. The best ones are often logs as they are usually plaintext, updated realtime, easy to access and you can usually pick out the patterns you want quite easily.
You do need to keep in mind though that some data may only be outputted at the end of the day or transaction in a format you can use so again I really recommend calling and asking.