This is one of those things where it just seemed like there should be a concise guide to accomplishing this. I couldn't find it. Hence, hopefully if you are struggling to figure this out for yourself, this makes your life easier. Further, at the end of this post, I list my references. If this does not provide enough information, you know where to find more!
Loosely, the steps to get the SAP HANA client libraries installed on Ubuntu 16.04 is to first stumble around on the SAP site long enough to finally figure out how to download the SAP HANA Client Software Packages, and curse liberally throughout this process. Second, install the packages.
Download and Install SAP Client
Figuring out exactly what you need to download, and where to download it from reminds me of trying to find something on the internet in 1996 - nothing is easy to find, and does not make any freaking sense. The only thing I can figure out is SAP does not want you to find the downloads. My experience was to start at the front page for SAP, and set up an account. This requires the normal sign up and confirm via email so they can now market to you. Once logged in, go to SAP Trials and Downloads, and look for SAP HANA Client Software Packages Download Page.
Somewhere along this path, to actually get the downloads, you will have to enable another level (yes, you must level up) in your account to actually get access to the downloads you are looking for, which will be available to another link emailed to you only active for a limited amount of time. No, I can't make up something as foolish as this process. Yes, it is a boatload of fun (not), and only took me the better part of an hour and a half to find and figure out. My loss equals your gain. Do it, get it, and do what I did, grab a beer.
Installation - Real Computer Stuff - Finally
After spending an inordinate amount of time doing something that should take no more than five minutes, you can now actually get about the business of getting your instance set up. This is actually the easy part. If you really want to cheat, just copy and paste this batch script I created to streamline the process. All you have to do is change the path to where the original zip archive is located.