To install, update og uninstall the SharePoint Online PowerShell module there are some few simple PowerShell commands you can use.

First of all, set your Execution policy to restricted

Get-ExecutionPolicy #for checking the current ExecutionPolicy setting
Set-ExecutionPolicy -ExecutionPolicy  Unrestricted

Install

 Install-Module -Name Microsoft.Online.SharePoint.PowerShell

Check current version

Get-Module -Name Microsoft.Online.SharePoint.PowerShell -ListAvailable | Select Name,Version

Update

Update-Module -Name Microsoft.Online.SharePoint.PowerShell

Uninstall

Uninstall-Module -Name Microsoft.Online.SharePoint.PowerShell