Getting started about fpga-litecoin-miner

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Are the same steps taken to get up and running with this project the same as the bitcoin version?

Pretty much the same, assuming you mean the Open Source Bitcoin Project on bitcointalk. You need some FPGA hardware, eg a development board or a supported bitcoin mining FPGA (currently Ngzhang's Lancelot/Icarus, Ztex quad 1.15y and Enterpoint Cairnsmore CM1). Prebuilt bitstreams are available for the supported boards, plus customised mining software (a hacked cgminer 3.1.1 and a python miner for the Lancelot/Icarus). Drivers and programming software are available from the manufacturers websites (though the Lancelot/Icarus also needs a Xilinx platform cable which is a little pricey for the official version).

If you want to do development work you need the relevant software which is a free (but large) download from Altera or Xilinx, but beware that the LX150 requires a license which is not free (in fact its extremely expensive), however a 30 day evaluation can be obtained from Xilinx. I wouldn't advise going this route unless you are an experienced FPGA developer though.

What is the best hardware in terms of cost per hashrate?

None. I do not recommend purchase of any FPGA hardware for scrypt mining. It's not economic. However if you already have the devices, then they will easily cover their running cost (electricity), though the actual profit will be small. Each LX150 FPGA will hash at around 15kHash/sec (which is tiny compared to what is available from a typical GPU).

Is there any docs on how to get it up and going?

Just the README's scattered around the githib, and the thread on litecointalk. You'll have to look in the experimental folder for the ztex 1.15y and cairnsmore CM1 ports. And you can ask here if there is anything specific you need help with.