Input forms

Is there any example of the forms API, I am a newbie at this and don't know where to start. I have looked at the form API, but can't find a demo/samples.

What I am looking for is to create a form where there are a dozen of choices, each one with a checkmark. The users can select any one, but they are limited to 3 of them in total + include their email address.

Maybe there is a better/simpler way of doing this than using the forms API. Please enlighten me.

Thanks