That's not too difficult if you understand Delphi's object model. A form is an object that descends from TObject, backed by a DFM file to make setting up the layout easier. The controls on it are other objects, and by default they're publicly visible to other objects from other units, like your other form. There are two ways to do this.
The easy way is to have your other form's code read the values from the controls directly once you're done with the first form. Just use stuff like MyString := Form2.EditBox.Text;
. This isn't particularly good style, but it works.
The right way to do it is to either put public properties on your form that will retrieve the values of the controls, or a function that will read them and return some sort of object or record containing all the settings. This takes a bit more work, but it results in cleaner code that's less likely to cause trouble if you modify things down the road.
EDIT: In response to the question in the comment:
To make one form show and hide another, you call Show and Hide on it. Or if you want it to show up in a modal dialog box, call the ShowModal method, which takes care of the hiding for you, as long as you create a button that sets ModalResult. (See the helpfile for details on how these methods work.)
Of course, the form has to have been created first. Either it can be autocreated by the DPR, which is good for simple programs but not so great once you get a lot of forms in your app, or you can create it in code. Henk has an example of how to do that, though I wouldn't recommend using the with keyword. And if you created the form yourself, make sure to Free it afterwards.