Vivado is the IDE that is used for the "programming" of Xilinx FPGAs. Xilinx/AMD together with Altera/Intel are the two dominant vendors for FPGAs. Programming the device in this context means generating the configuration of the FPGA so that it implements some logic specified by the designer.
Vivado is a 70GB install and quite a piece of software. I'll try to give an orientation on how to use Vivado and give a high level conceptual and architectural overview of the system. Theand the work flows that are designed into the tools (and seem to have been widely adopted in the FPGA industry). There are many different ways for using Vivado but as I am a command line kind of person, I will of course look at how to script things as much as possible.