Use a systematic approach. what are the big pieces? serial I/O to PC, PIC to PC protocol, data acquisition, control module? There maybe others, I don't know your project at all. draw a block diagram. Then take each block and try to detail it out. Maybe make sub-blocks. Think about how data will flow. At this point you should be getting a sense of the areas that you need to learn about.
I can pretty much see that serial I/O is one of them - there are lots of resources out there that will help you get up to speed on the UART in the 877.
You should also spend some time detailing out the type of information that will be passed between the PIC and the PC (AKA Protocol). try to understand how data wil flow. command from PC to PIC, for example.
edit: oh yeah, have you figured out what you are going to program in? C? ASM? BASIC? you might want to put some thought into that early.