Okay, so if you're following along from Part 1, you now know where your nearest bus stop is, what lines serve it, and where those lines go. Now I'd like to direct your attention to the remainder of the transit system. You need not memorize the whole map, but it's a good idea to familiarize yourself with major lines and transfer points, just as you'd familiarize yourself with major roads and freeways in your town. So take a moment now to look at those system maps I posted last time (RTA, Omnitrans). What you're looking for are major transfer centers (marked as "T" on RTA's map and "TC" on Omni's), which should list the routes that serve those points. Find the transfer points that are served by your local bus routes.
Another thing to look for are frequent bus services, lines that you can use without looking at the schedule to see when they're coming, and therefore can count on for spontaneous trips around the city. (In a decent transit system, these routes come every 15 minutes or better, but since few such routes exist out here, I loosen the definition to 20 minutes myself.) Frustratingly, none of our local transit agencies does any sort of frequent network mapping, and actually finding out what routes in your area qualify would require going through a lot of individual timetables. So I'll do that for you.
On RTA's system, routes 1 (University Ave-Downtown-Magnolia Ave) and 16 (Downtown-University Ave.-Canyon Crest-Moreno Valley Mall) run every 20 minutes or better. 15 runs every 40 minutes, and most everything else is hourly or worse.
On Omni's system, in the West Valley, routes 61 and 66 are frequent. In the East Valley, 1, 2, 3/4, and 14 are frequent. Many other routes are half-hourly.
All of these calculations are based on weekday mid-day frequencies, and service can get a lot worse on the weekends.
Finally, you'll want to look for express service. Express service is usually extremely limited in terms of frequency, but can be useful due to its speed. Metrolink is an express service, as is RTA's CommuterLink system (routes with 200-series route numbers), and Omnitrans' route 90. Most of these services stop at major transit centers (or, in the case of Metrolink, train stations).
Knowing these details will give you a good idea of what the transit system around you looks like, so you can see ways in which you could use it for upcoming trips.