Follow the Instructions linked on the xAct Homepage first to load the main xAct package, which contains the Invar kernel. Then, the database of Riemann relations in Invar must be downloaded and installed separately. Follow the Invar link on the xAct page, and on the Invar page there is a Readme link that provides detailed instructions on the special install of the Riemann relations. You should also check at http://contrib.xact.es (link on xAct page provided) for possible contributing packages updates since the main xAct package was created, such as a whole new xPrint version and updates to xTras. Some of these have a link to another webpage for updating, and others provide a GitHub page where you can download the changed files (only overwrite the ones that have changed since the main xAct package was created).
The xAct folks recommend installing xAct in the Applications folder of the MMA $UserBaseDirectory (just unzip into this folder), which should (hopefully) remain untouched when updating MMA. After all the effort required to get to a fully updated xAct package, I would recommend storing a backup of it in case it gets messed up during an MMA update.
Trying to get the xAct help files installed in MMA 10 and higher seems to be a "lost cause." Besides, the xAct developers say that the help directory in the main xAct package does not reflect all of the more recent changes in the contributed packages. They recommend just going directly to the documentation files, which are mainly notebooks (I store a copy of them all next to my MMA working folders for easy access). Also, the xPrint palette has a help menu getting to the main help files (which is up to date if the latest xPrint version is installed).
xAct has its own GoogleGroups forum, which has a lot of info. on both installation issues as well as how to use it. For instance, I wanted to define a flat metric, but xAct generated MMA error messages when building it. Running a search under "FlatMetric" (the xAct option to specify a flat metric), there was a thread ("Mathematica 11.1") where the main developer suggested changing an entry in one of the files if you didn't want to see the error message (otherwise he said to ignore it). So there is an "update" to the installation that doesn't show up anywhere but as an xAct forum entry.
Run Needs["xAct`xPrint`"] followed by Needs["xAct`xTras`"] to load up "everything" when using xAct (except for specialized contributed packages which must be additionally loaded). IMO, the quickest and easiest way to start learning xAct is to first go through the xPrint instruction notebook xPrintDoc.nb, and then use xPrint when possible.
Hopefully that about covers it.