How are you sending your web forms? If you are using WordPress or some other CMS, I can't really help. I know there are plugins for those that will provide you a solution.
If you are using PHP, then make sure you are declaring your email headers. This would/should help with any blocking that might be going on...
Great and easy place to learn:
The more technical way to learn something...straight from the source:
Here is an example (W3Schools) that with an email in the from and cc spots.
$to = "email@example.com";
$subject = "My subject";
$txt = "Hello world!";
$headers = "From: firstname.lastname@example.org" . "\r\n" .
You can also use the users email they fill out on the form for the from header. This should allow you to reply to them from the message sent from the form.
Has an ok example.
Google will provide countless contact form examples. I suggest going to W3Schools and learning how to write your own so that it will meet your exact needs.