You can deploy Apps Script as a Web App [1]. You'll need to create a html file [2] in which you'll put the form you want. Here [3] is well explain how to execute Apps Script functions with JavaScript in the html. Finally, in an Apps Script function you can use the SpreadsheetApp class to insert the values you want [4].
This would be an example code found on the documentation:
Index.html
<!DOCTYPE html>
<html>
<head>
<base target="_top">
<script>
// Prevent forms from submitting.
function preventFormSubmit() {
var forms = document.querySelectorAll('form');
for (var i = 0; i < forms.length; i++) {
forms[i].addEventListener('submit', function(event) {
event.preventDefault();
});
}
}
window.addEventListener('load', preventFormSubmit);
function handleFormSubmit(formObject) {
google.script.run.withSuccessHandler(updateUrl).processForm(formObject);
}
function updateUrl(url) {
var div = document.getElementById('output');
div.innerHTML = '<a href="' + url + '">Got it!</a>';
}
</script>
</head>
<body>
<form id="myForm" onsubmit="handleFormSubmit(this)">
<input name="myFile" type="file" />
<input type="submit" value="Submit" />
</form>
<div id="output"></div>
</body>
</html>
code.gs
function doGet() {
return HtmlService.createHtmlOutputFromFile('Index');
}
function processForm(formObject) {
var formBlob = formObject.myFile;
var driveFile = DriveApp.createFile(formBlob);
return driveFile.getUrl();
}
[1] https://developers.google.com/apps-script/guides/web
[2] https://developers.google.com/apps-script/guides/html/
[3] https://developers.google.com/apps-script/guides/html/communication
[4] https://developers.google.com/apps-script/reference/spreadsheet/spreadsheet-app