Normally, Teams runs in Per-User mode. That is to say, Teams is installed directly into the users profile area, can be installed without admin rights, and updates are also applied automatically with no admin rights. Microsoft do make a per-machine mode installer available, but it's only supported for use in VDI environments. If your organisation requires it, perhaps because you don't allow executables to be run from user profile locations, this installer does also work locally. Be warned, however, that if you run into any client related issues, Microsoft's response is likely to be "Call us back when you have a supported configuration"
One of the significant issues I noticed when running Teams in per-machine mode is that Office (in my case, Office 2016) requires the Skype for Business client to be installed for Outlook to display the presence indicator next to contacts names. If you're migrating to Teams and have been forced down the per-machine mode route, you won't notice this until you start to decom your Skype platform and remove the Skype client from users machines.
After a week or two of digging around in various places, I managed to get this working using the following method. You'll need a copy of REGTLIB.EXE - you may need to raise a case with Microsoft to get a hold of this tool.
First of all, copy the following files from your Teams installation folder to your Office installation folder (i.e. the same folder where outlook.exe lives):
Then, in a command prompt window, run the following command (adjust the path to suit the actual location of the .TLB files):
REGTLIB "C:\Program Files\Microsoft Office\Office16\Uc.tlb"
REGTLIB "C:\Program Files\Microsoft Office\Office16\Uc.win32.tlb"
Restart Outlook, and Presence should be magically working again. I hope this saves you from repeating some of the work I had to do to figure this out.