Create a script with a Send Mail script step.
In the options, the "Send via" option can be set to either E-Mail client, or SMTP Server.
if it's set to Email Client it will open up the Email program installed on the users machine (i.e., Outlook), and opens a new message, that the user can see, modify and send, or cancel.
SMPT Server requires you knowing a few more settings, but can be set to send an email without user interaction. It will not appear in their Sent items, as it would have been sent directly from the mail server, not the email client.
Then right click on the field that you want notification of when it gets changed, click Set Script Triggers, and set the script to be triggered OnObjectValidate.
Unless users hardly ever modify data, this sounds like a recipe for getting a ton of emails everyday. Can't help thinking that a nightly script that generates and emails a list of the modified records might be much easier to work with...
Thanks Phil_1986, I got it working with your suggestion.
PhilModJunk is right that we will get tons of emails everyday, how do I generate a list of modified records for emailing?
My thoughts would be to make sure you have a field that captures the modified date. Pretty simple just create a field with an auto enter, and in the options select Modification | Date and make sure the field is of type Date. Then on your script have it perform a find of any records that have a modified date of the current date.
You could also create a field that logs changes of any data in any field. Nightwing has a really good example of one here