I think what you want is a <form> to appear inside a modal window.
This is a bit advanced. How good are your coding skills?
As far as the Modal Window goes, you can use a jQuery UI Dialog for that. The code follows below. Copy & paste this into a new blank document. Save as test.html and preview in a browser.
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>jQuery UI Dialog + Animation</title>
<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css">
</head>
<body>
<button id="opener">Click to Join Email List</button>
<div id="dialog" title="Email Form">
<form action="your-form-to-email-script.php">
<p>
<label for="name">Name:</label>
<input type="name" id="name" required placeholder="First & Last">
</p>
<p>
<label for="email">Email</label>
<input type="email" id="email" required placeholder="yourname@domain.com">
<br>
</p>
<input type="submit" value="Submit">
</form>
</div>
<!--jquery code library-->
<script src="https://code.jquery.com/jquery-1.12.2.min.js" integrity="sha256-lZFHibXzMHo3GGeehn1hudTAP3Sc0uKXBXAzHX1sjtk=" crossorigin="anonymous"></script>
<!--jQuery UI library-->
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<!--invoke dialog function on page load-->
<script>
$( function() {
$( "#dialog" ).dialog({
autoOpen: false,
show: {
effect: "blind",
duration: 1000
},
hide: {
effect: "explode",
duration: 1000
}
});
$( "#opener" ).on( "click", function() {
$( "#dialog" ).dialog( "open" );
});
} );
</script>
</body>
</html>
It goes without saying, you'll need to provide your own form processing script in a server-side language that's supported by your web hosting plan.
Nancy