There are many changes with Google Forms but the big change is that Forms is now its own editor. It has the ability to talk to Google Sheets, but should now be considered a single editor. Therefore, now when someone submits your Form the responses are actually stored in Forms itself and not necessarily a spreadsheet. Google gives you this option with the response destination feature. You can either keep the responses stored in the Form (which allows only a summary view) or link them to a new or existing spreadsheet to see each individual response. There is a nice button and wizard in the form editor to help with this.
The biggest questions on the forums right now tend to revolve around the difference between an editor/owner/collaborator and respondents (Google's term for people who fill out the form). I recommend keeping your Form always with sharing settings of Private. This setting affects the editor/owner/collaborator. By keeping the sharing settings at Private, you can easily collaborate with others on the content of the Form just as if it were a Google Doc or Sheet (also in real time). Only those who have explicit access to edit the form will be allowed to edit the form. Respondents can access the form to fill it out using the Send form feature. You will find this blue button in the upper right of the editor or at the very bottom. When you click here you find a few options for sending your form to respondents. The easiest method is the URL that is generated that goes to the life form. You can paste this link on a website, on your Google+ page, a Facebook page, in an email, etc. When people click on it they will be taken to your Form to fill out as a respondent (There might be a bug right now with some users having to be signed into a Google account, but I have yet to find this consistent behavior or able to reproduce...there might be some user error here).
There are lots of cool little features but my favorite is the ability to copy a list of multiple choice answers from a spreadsheet and paste it into the form editor in one quit click. Make sure to use Ctrl+C and Ctrl+V when doing and make sure your cursor is in the first box for the multiple choice question.
Other big topics include the fact that the number of themes are limited and there is currently no feature for adding pictures on a form but hang in there!
Enjoy the new Forms and if you have any questions or feedback make sure to head over to the Google Docs Help Forum.