How do I remove the "Learn More" verbiage next to each product, yet still allow the user to click on the image to go to the product details page?
This comes from the catalog/product/list.phtml template. Depending on the theme you are using that will be somewhere like app/design/frontend/rwd/default/template/catalog/product/list.phtml, or app/design/frontend/base/default/template/catalog/product/list.phtml.
To remove the link you could edit one of those files but better practice would be to override the template in your sites theme and change it there e.g app/design/frontend/mypackage/mytheme/template/catalog/product/list.phtml
To override a theme, say you were basing your theme on the rwd theme, you could create a new theme folder, lets say it was app/design/frontend/mysite/default. In that theme you should create a new file called etc/theme.xml, that file would look something like this:
<?xml version="1.0"?> <theme> <parent>rwd/default</parent> </theme>
It is basically saying that your new theme extends the rwd/default theme. Then set the package in the admin design settings to mysite rather than rwd. Your site will now be using your new theme. You can then override templates by replicating them in you theme template directory, so in this case app/design/frontend/mysite/default/template/catalog/product/list.phtml.