Why is this better than using a normal search engine?
Keep in mind that there is no guarantee spelling is 100% consistent. So, for example, if you're interested in mentions of Starbase 47, it's advisable to search for both "Starbase 47" and "Starbase fourty-seven". The same applies to possibly abbreviated words like "Deep Space 9" vs "DS9".
There are two interfaces available to you. The easy interface simply lets you input what you’re looking for without any prior knowledge requirements. The advanced interface on the other hand allows to manually enter a query using the syntax described there. While that is considerably more difficult to use, it allows queries of arbitrary complexity. It also gives access to regex-based search operations and special parameters.
Many thanks to Chrissie at Chakoteya for making her transcripts available for this - and for typing them all out in the first place!
Many thanks also to reddit's /u/Algernon_Asimov!