Actually, it's very easy but took me a while to figure out as well. Use the Acrobat Forms Document Format (FDF). Here's some quick code that'll build it from an array of key=>value pairs. Could work the same with HTTP_POST_VARS:
$fdfdata = "%FDF-1.2\n%’“¦²\n";
$fdfdata .= "1 0 obj \n<< /FDF ";
$fdfdata .= "<< /Fields [\n";
//loop that adds the field names and values
foreach($values as $key=>$val)
{
$val=str_replace("(","\\(",str_replace(")","\\)",$val));
$fdfdata.="<< /V ($val)/T ($key) >> ";
}
$fdfdata .= "]\n";
$fdfdata .= "/F ($FULL_PATH_TO_PDF_FORM) >>";
$fdfdata .= ">>\nendobj\ntrailer\n<<\n/Root 1 0 R\n>>\n";
$fdfdata .= "%%EOF";
/*** Now we display the FDF data which causes Acrobat to start ***/
header ("Content-Type: application/vnd.fdf");
header ( "Content-Disposition: inline" );
print $fdfdata;
