There are two ways to save the data:

At the "Save Contact Data" window, you'll need to save the Dropdown title and dropdown options. Sometimes, the name that you call the title and the options on the back-end may not be the same as what your subscribers see on the form/landing page.

For example, the dropdown title is "How did you hear about us?", and this is for subscribers. I'll simply call it "Source" in my back-end.

Then name the dropdown options in your back-end. It can be the same or different from what your subscribers see. It all depends on your needs.

Once the subscriber selects an option from the dropdown, the value will be saved under the Custom Field, like this:

At the "Save Contact Data" window, you'll need to save the checkbox options. These options will be saved as tags on your contacts. Sometimes, the name that you call the options on the back-end may not be the same as what your subscribers see on the form/landing page.

For example, I have a checkbox option called "Weekly updates". I will call this tag "Interest: weekly updates" in my back-end.

Once the subscriber selects options from the checkbox, the value will be saved as a tag on the contact, like this:

To learn more about adding custom fields in a form/landing page, read this tutorial here.