I have performed a very basic search and then saved it with a specific name. How/where do I go to retrieve this saved search?
If you're in the standard 'Search' app, which you probably are, you should see a menu option called 'Searches & Reports'. Click that and in that menu you should see the name of the search you saved. Click it there to rerun it.
You can also use Splunk's search language to return the results of a saved search via:
| savedsearch <savedsearchname>