See New Features Rolling Out Soon
Under Google Docs, Click Create New.
Select Form.
Create the form questions that you want.
Click RESPONSES and click the spreadsheet icon.
A spreadsheet will be created that will store the form responses. Open that spreadsheet, Click the Tools menu and select "Notification rules...".
Create a rule. Under "Notify me at [your address] when..." put a check in "A user submits a form" and either "Email - daily digest" or "Email - right away". See 'Notification to Multiple Addresses' below.
Save the rule.
Go to your site and on the page where you want the form. In the Insert menu click Forms in the Google Docs section.
Select the form you just created.
Save the page.
Notice that under step 6 you will be notified that someone has submitted your form, and then you have to open up the spreadsheet to see what they entered.
If you want to use this as a comment form where the comments are posted on your site click Share while editing the spreadsheet and select to share it to the public and on the File menu select Publish to the Web and to automatically re-publish when changed** and click Publish as a web page. Insert the spreadsheet itself as shown below. In the INSERT menu select Sheets in the Google Docs section and select the spreadsheet associated with your form.
Note that the spreadsheet will not automatically update. A viewer will have to refresh the page in order to see new comments and there may be a delay of up to 5 minutes before the new comment appears.
Also if you want to remove the formatting that new forms has added you can revert to the old version as I have done. See this forum post for help on doing that.
**If you want to moderate the comments do not select automatically re-publish, When you get notified someone has posted you can the publish it. File, Publish to the web, Republish now.
Notifications normally go the owner's email. Here are suggestions for sending to multiple people.
In Gmail, set up a filter to forward to the other account(s) or add this add-on.
Add-ons in Forms have features to send notifications to multiple emails. From the form edit view, click the form's 3-dots menu, Add-ons, search for notifications.
This add-on allows users to automate email notifications for:
1. Form respondents - Configure messages that are delivered as individuals submit the Forms submission
2. Form owners and editors - Configure messages that are delivered to you (as the creator of the Form), or other collaborators, on predetermined response thresholds.