Change my form design

How can I change my form design (https://form.jotform.com/53165272735962) to look more like: https://partners1.geico.com/MCRForm  ?

You'll probably need to use the Form Designer Tool and a knowledge with CSS to make your form have that specific design. Here are some links that might help:

Form Designer Tool guide: http://www.jotform.com/help/300-Form-Designer-Tutorial-Let-s-create-fantastic-forms- 

CSS Tutorial on W3Schools: http://www.w3schools.com/css/ 

Customize your Form using custom CSS code: http://www.jotform.com/help/75-Customize-your-Form-using-Custom-CSS-Codes 

I made a quick look at your form and this is the the changes that I was able to make with reference to the website you shared: https://form.jotform.com/53205024999964?. It is possible but may take some time for you to have all design to be implemented. Please do visit the links for the Form Design Tool and CSS I shared above.

I hope that helps.