How do I find out how many times the word "agape" (or any other word) is in scripture and which verses it is in?
The easiest way is to start from one occurence where you know it is, right click on it, make sure the Lemma tab is selected on the right-hand side of the context menu, and choose "Search this Resource" on the left-hand side.
But here's how to generate an Englishman's Concordance which will accomplish the same goal, though also showing you all the ways that word is translated in English:
http://wiki.logos.com/Englishman's_Concordance
EDIT: Another important tool in Logos 4 which will give you the answer is Bible Word Study (on the Guides menu).
Type in g:agape to find the Greek spelling that matches that transliteration, and select it from the dropdown menu.
Then hit Enter (or click the blue arrow). That will bring up the BWS with its Translation Ring, among other things. The Translation Ring shows the different words that are used in English to translate that Greek word.
Click on either translation to show all those occurrences in place in Scripture (and their count), or click in the center of the ring to show ALL occurrences of all translations, with their counts:
Chad,
You need to do a Bible search to do this. As you're new to Logos, can I recommend this first steps video, together with the ones on searching and reverse interlinears that you'll also find on that page.
But for this particular search, go to Search, Choose Bible Search from the right hand side. The choose which Bible version you want (or choose Top Bibles or All Bibles), then type: g:agape and click on the suggested Greek word (the 'g' stands for Greek). The click the blue arrow to the right, or press enter to perform the search.
Mark