Setting variables in PowerShell itself is trivial, merely assign (= operator) to the variable:

$VarName = 42

But likely the question is looking for a way to set Environment variables which the (VSTS) application can 'see' and 'use' when it is called from PowerShell.

To assign to any session Environment variable prefix the name with "ENV" so it looks like this:

$Env:VarName = 4201

This will remain for the current PowerShell session or life of the console -- other sessions in other windows or run later will not see or be affected by such settings.

If you wish to have a persistent Environment variable then you must set that in the registry, either for the User (HKey_Local_User) or Computer (Hkey_Local_Machine).

These will get the environment settings from the registry (maybe be different that currently set in your process):

[Environment]::GetEnvironmentVariable('path',[EnvironmentVariableTarget]::Machine)
[Environment]::GetEnvironmentVariable('path',[EnvironmentVariableTarget]::User)

And the Set commands are similar but include the new value (e.g., variable 'Tools' is set to 'C:\':

[Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::Machine)
[Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::User)

There is also a "location" enumeration for "Process" (instead of User or Machine) but it is simpler to set this using the PowerShell $Env:VariableName shown above.

    [Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::Process)

Setting variables in PowerShell itself is trivial, merely assign (= operator) to the variable:

$VarName = 42

But likely the question is looking for a way to set Environment variables which the (VSTS) application can 'see' and 'use' when it is called from PowerShell.

To assign to any session Environment variable prefix the name with "ENV" so it looks like this:

$Env:VarName = 4201

This will remain for the current PowerShell session or life of the console -- other sessions in other windows or run later will not see or be affected by such settings.

If you wish to have a persistent Environment variable then you must set that in the registry, either for the User (HKey_Local_User) or Computer (Hkey_Local_Machine).

These will get the environment settings from the registry (maybe be different that currently set in your process):

[Environment]::GetEnvironmentVariable('path',[EnvironmentVariableTarget]::Machine)
[Environment]::GetEnvironmentVariable('path',[EnvironmentVariableTarget]::User)

And the Set commands are similar but include the new value (e.g., variable 'Tools' is set to 'C:\':

[Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::Machine)
[Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::User)

There is also a "location" enumeration for "Process" (instead of User or Machine) but it is simpler to set this using the PowerShell $Env:VariableName shown above.

    [Environment]::SetEnvironmentVariable('Tools', 'C:\', [EnvironmentVariableTarget]::Process)

When defining variables in PowerShell, single quotes (') mean you want the literal version of the string. Use double-quotes (") if you want to allow variable expansion:

PS C:\> $a = "hello"
PS C:\> $a
hello
PS C:\> $b = "$a world!"
PS C:\> $b
hello world!

More info:

• Single Quotes vs. Double Quotes in PowerShell: What's the Difference?
• Referencing Variables and Variable Values

Edit after comments:

For your example where you're pulling the line from a file, that's a little trickier since it's pulling the line as a literal string.

The easiest way (IMO) would be to use the Replace method; something like:

$selHost = (get-content c:\scripts\hosts.txt)[0]
$a = ((get-content c:\scripts\config.txt)[1]).replace('$selhost', $selHost)

The variables are created in your function's local-scope. Those variables are deleted when your function is done.

Global: 
    The scope that is in effect when Windows PowerShell
    starts. Variables and functions that are present when
    Windows PowerShell starts have been created in the
    global scope. This includes automatic variables and
    preference variables. This also includes the variables, aliases,
    and functions that are in your Windows PowerShell
    profiles.

Local:  
    The current scope. The local scope can be the global 
    scope or any other scope. 

Script: 
    The scope that is created while a script file runs. Only
    the commands in the script run in the script scope. To
    the commands in a script, the script scope is the local
    scope.

Source: about_Scopes

If you need the variables to be available for the script, then write them to the script scope.

$BackupFile = $null
$TaskSequenceID = $null
$OSDComputerName = $null
$capturedWimPath = $null

Function Set-OsToBuild 
{
  switch ($OsToBuild)
  {
    "Win7x64"
        { 
            $script:BackupFile = "Win7x64-SP1.wim"
            $script:TaskSequenceID = "WIN7X64BC"
            $script:OSDComputerName = "Ref-Win7x64"
            $script:capturedWimPath = "$($PathToMdtShare)\Captures\$BackupFile"
        }
  }
}

If you would like to keep the values for whole sessions (until you close the powershell-process), then you should use the global scope.

$global:BackupFile = $null
$global:TaskSequenceID = $null
$global:OSDComputerName = $null
$global:capturedWimPath = $null

Function Set-OsToBuild 
{
  switch ($OsToBuild)
  {
    "Win7x64"
        { 
            $global:BackupFile = "Win7x64-SP1.wim"
            $global:TaskSequenceID = "WIN7X64BC"
            $global:OSDComputerName = "Ref-Win7x64"
            $global:capturedWimPath = "$($PathToMdtShare)\Captures\$BackupFile"
        }
  }
}