Invoke-WebRequest, POST with parameters
Put your parameters in a hash table and pass them like this:
$postParams = @{username='me';moredata='qwerty'}
Invoke-WebRequest -Uri http://example.com/foobar -Method POST -Body $postParams
For some picky web services, the request needs to have the content type set to JSON and the body to be a JSON string. For example:
Invoke-WebRequest -UseBasicParsing http://example.com/service -ContentType "application/json" -Method POST -Body "{ 'ItemID':3661515, 'Name':'test'}"
or the equivalent for XML, etc.