Variables and Operators

In PowerShell, all variable names start with the “$” character.
Creating a new variable can be done in several ways:

$MyVariable = SomeValue
$MyVariable = "Some String Value"
[DataType]$MyVariable = SomeValue
New-Item Variable:\MyVariable -value SomeValue
New-Variable:\MyVariable -value SomeValue

Variable names containing punctuation, can be handled with the syntax ${MyVari@ble} = SomeValue
However if the braces ${ } contain a colon ":" then powershell will treat the variable as a PATH and store the values directly in that file.
${C:\some_file.txt} = SomeValue

Operators allow you to assign a value to the variable, or perform mathematical operations:

  Operator   Description

     = n     Equals n
    += n     Increase value by n (for strings will append n to the string)
    -= n     Decrease the value by n
    *= n     Multiply the value by n (for strings, duplicate the string n times)
    /= n     Divide the value by n
    %= n     Divide the value by n and assign the remainder (modulus)

  Arithmetic operators:
    + Add, - Subtract, * Multiply, / Divide, % Mod(Remainder from a division)

Powershell will follow normal arithmetic precedence working left to right, parentheses can be used override this.

Examples

$myPrice = 128
$myPrice += 200
$myItem = "Barbecue grill"
$myDescription = $myItem + " $ " + $myPrice

$CastAsString = "55"
$myHexValue = 0x10
$myExponentialValue = 6.5e3

Strongly typed:
[int]$myPrice = 128
[string]$myDescription = "Barbecue grill"
[string]$myDescription = 123
[string]$myDate = (get-date).ToString("yyyyMM")
$([DateTime] "12/30/2009")
$([DateTime]::Now)
[datetime]$start_date=[datetime]::now.date.addDays(-5)

When creating strongly typed variables it's a good idea to indicate the datatype in the variable name: $strProduct or $intPrice

Array variables:

$myArray = "The", "world", "is", "everlasting"

Powershell can also assign values to multiple variables:

$varX, $varY = 64
$varA, $varB, $varC = 1, 2, 3

That will assign 1 to $varA, 2 to $varB, and 3 to $varC.

Script blocks

An entire script block can be stored in a variable: $somevar = { a bunch of commands }
Then execute the script using &
&somevar
Most times you will want to take this a step further and just turn the script block into a Function or Filter.

Reserved Words - the following may not be used as identifiers (unless surrounded in quotes)
break,continue,do,else,elseif,for,foreach,function,filter,in,if,return,switch,until,where,while.

“Most variables can show either an upward trend or a downward trend, depending on the base year chosen” - Thomas Sowell

Related:
Reference variables - Change the value of a passed variable
Get-Item Variable:
Clear-Variable - Remove the value from a variable
Get-Variable - Get a powershell variable
New-Variable - Create a new variable
Remove-Variable - Remove a variable and its value
Set-Variable - Set a variable and a value