Methinks you may be having trouble because of the single quotes. Since you're using single quotes to encapse your query, you will need to \ you single quotes around your values. Or, I would suggest, use double quotes to encapse your query. Like this...
$sql = "INSERT INTO `yamaha cruisers`
(`buyer`,`purchase_date`,`warranty`,
`recieved_date`,`year`,`model`,
`vin`,`color`)
VALUES
('$buyer','$purchase_date','$warranty',
'$recieved_date','$year','$model',
'vin','color')";
And even better yet, escape the string when referencing a variable.
$sql = "INSERT INTO `yamaha cruisers`
(`buyer`,`purchase_date`,`warranty`,
`recieved_date`,`year`,`model`,
`vin`,`color`)
VALUES
('".$buyer."','".$purchase_date."','".$warranty."',
'".$recieved_date."','".$year."','".$model."',
'vin','color')";