How to make content creation form more organized. Taxonomy Checkbox list
If you are familiar with using CSS to change the layout of your drupal site already, something like this should work:

/* Make categories field 2 columns */

div.form-item.form-type-checkboxes.form-item-field-categories-und {

    -moz-column-count: 2;
    -moz-column-gap: 20px;
    -webkit-column-count: 2;
    -webkit-column-gap: 20px;
    column-count: 2;
    column-gap: 20px;


}

If not, it will depend on what theme you are using. We are using the seven theme for our admin pages, which include the node create pages. In the seven theme, I could just add the chunk of CSS above to the style.css file. Technically however, this chunk probably shouldn't be added into a core theme because it might get wiped out when/if you upgrade drupal core. 

If you want to do it properly, you should create a new stylesheet with something similar to the CSS chunk above and give it a name. Then, add that stylesheet in your theme's .info file. (You can see specific instructions on how to do that here: https://drupal.org/node/171209)

Be sure that you don't have your CSS optimized when you are updating your stylesheets. If you aren't sure how to check this setting, go to admin/config/development/performance and make sure the option to aggregate and compress CSS isn't checked.

Without knowing more about your setup, what theme you are using, etc. it's hard to make a more specific recommendation.