The script you are wanting is going to do two things. First, we will download a file and store it in an accessible location. Second, we will then run the executable with whatever arguments we need to have it install successfully.

Step 1:

We have two ways of accomplishing this task. The first is to use Invoke-Webrequest. The only two arguments we need for it will be the URL of the .exe file, and where we want that file to go on our local machine.

$url = "http://www.contoso.com/pathtoexe.exe"
$outpath = "$PSScriptRoot/myexe.exe"
Invoke-WebRequest -Uri $url -OutFile $outpath

I use $PSScriptRoot here because it will let me drop the exe right next to where the Powershell script is running, but feel free to put a path of your choice in, like C:/temp or downloads or whatever you want. You may notice that with larger files, the Invoke-WebRequestmethod takes a long time. If this is the case, we can call .Net directly and hopefully speed things up.

We will set our variables of $url and $outpath the same, but instead of Invoke-WebRequest we will use the following .Net code:

$wc = New-Object System.Net.WebClient
$wc.DownloadFile($url, $outpath)

Step 2:

Calling an executable is the easy part.

$args = @("Comma","Separated","Arguments")
Start-Process -Filepath "$PSScriptRoot/myexe.exe" -ArgumentList $args

And that should just about do it for you.