How can I stop and start individual websites in IIS using PowerShell?

Just for future quick reference, the commands are:

Import-Module WebAdministration
Stop-WebSite 'Default Web Site'
Start-WebSite 'Default Web Site'

Adding to Keith's answer, you can perform this remotely using Invoke-Command.

Import-Module WebAdministration
$siteName = "Default Web Site"
$serverName = "name"
$block = {Stop-WebSite $args[0]; Start-WebSite $args[0]};  
$session = New-PSSession -ComputerName $serverName
Invoke-Command -Session $session -ScriptBlock $block -ArgumentList $siteName 

To get access to system modules, Powershell needs to be run like this:

[path]\powershell.exe -NoExit -ImportSystemModules

I found the above on this iis forum.

I found that the following to stop individual websites on a remote server to work:

Invoke-Command -Computername $servername -Scriptblock { 
    (Import-Module WebAdministration); 
    Stop-Website -Name "WebsiteName"; 
    Stop-Website -Name "AnotherWebsiteName"
}

I had some of the errors above until Import-Module was put in ()