If you mean by taking taxis you have to ask the taxi driver for the fapiao. Just say fapiao to the driver and he will give you one. Once you collect all your fapiaos together you can give them to your company and they should pay you back. 

In China, while it is common when you purchase items to get a fapiao (receipt), it is not normally given for services render, like a taxi, a restaurant, even some smaller hotels.  So, you must request one when asking for the bill and paying it, and they are "suppossed" to give you one.`
Please, do not ask me why things work this way, I have no idea, maybe just being plain lazy sometimes.

The way I read the question was - HMO needs to provide an invoice to the company, so they can pay the agreed amount for his/her labour. NOT for receipts for taxis, meals, etc... Am I right, HMO??

And, if so, I can't really help you with a legal one. I presume you are working here legally? (btw, you can get fake ones from various places, including via the internet.)

(btw, in reference to the above, by law, if someone requests a fapiao, they must give it! Of course, no-one really cares about the law here :( )

You need to have a legal registered business in order to issue fapiaos.  If you are doing freelance work and are not a registered company, I hate to say, but your only option is to find either a company willing to issue one for you or to get a fake one.

excuse to screw you over on the payment. (my uneducated guess)

Just tell the person attending or driving you "fapiao" or "gei wo fapiao". Word of advise: do NOT ask for one in the pink lighted barbershop...