If you do not already have a website for this module, for Drupal 6 you can download the UberDrupal installation profile. This contains Ubercart and all the other necessary modules. For Drupal 7 you will need to set up Drupal and Ubercart. Once the store is set up go to modules and turn on Attribute. Install uc_dropdown_attributes and go to modules and turn it on. Go to a product and edit it. There should be the following tabs: product, attributes, dependencies, options and adjustments. Go to the attributes tab and create a couple of attributes. Create options for each of the attributes. Add the attributes to the product. Now we are ready to define the attribute dependencies. Click on the dependencies tab. For each dependent attribute choose the attribute it depends on. The possible values for the attribute it depends on are displayed. Choose for which values you want the dependent attribute to appear. Save the dependencies. Then view the product and check to make sure the attributes are displayed when the appropriate value of the other attribute is selected.
The cart will display attributes that have a selected option. If the attribute is not required then it has a default selected option and will appear in the cart. For dependent attributes that may not be presented to the user this may not be what you want. Go to the dependencies tab and check the required box for the dependent attribute(s). Then the attribute will not have a default option and it will not appear in the cart if it was not displayed when the product was added to the cart.