If the form and pages are already created, just skip to the "Set up Email Notification" section to have new form emails sent to you.
Creating the form
First you must go into your Google Drive and create a "Form" type document. This is accessible at drive.google.com.
Create your form and add any fields you would like to use. Text, checkbox, multiple choice, etc. fields can be added. Use the Add Item button in the upper left to add various questions for the user to submit.
Once the form is complete then make sure it is saved (upper right).
Now to start the web-embed process, go to See Responses --> Spreadsheet. This will open the response spreadsheet. Go to the "Share" tab in upper right, and change the settings to Private so that the public cannot view the responses. Then, add any users (or the root user) so that people who need to see the results can view them.
Make sure it's saved again.
Embedding in a webpage
If necessary, make a new Google site page to house your form. Then, click Insert from admin toolbar --> Spreadsheet Form. Your new form should automatically show up in the list of options. Select it, change any settings as desired, and click Save.
Set up Email Notification
Go back to the spreadsheet through drive.google.com, and open it to see all responses (a new form will be empty except for data headers). Select Tools --> Notification Rules from the menu.
Check the box for "a user submits a form", and then select between Email - Daily Digest and Email - right away as per your preference. (If you expect lots of user hits in a single day, daily digest may be better so that your inbox isn't flooded. However if something requires a prompt response with occasional use, right away is the better choice.) Save the settings.
Viewing submitted forms
You can open the spreadsheet at any time to view submitted forms. You may also delete or change the entries in the spreadsheet manually. New submittals will always add a new line to the form.