Purpose of the plan vs. your interests
This looks like the "Berkshire Valley Lines" from Atlas' HO King-Size Plan Book with a couple of small modifications. Few, if any, of the plans in the Atlas books are designed for engaging operations. (A cynic might argue that they are primarily designed to sell Atlas track -- and in that, they are most successful.)
What you have constructed so far is primarily intended to allow a train or two to be built up in the yard, run a few laps on the mainilne, and return to the yard. Trains could switch the spurs that you have, and you could add a couple more. Unfortunately, the track plan as constructed doesn't offer a lot of potential for the kinds of long-term engaging challenge many people find most interesting.
Many plans designed from the beginning for operation suggest "somewhere else" for trains to run to and from. This is typically called "staging" and is what gives the impression of connecting to a larger outside world beyond the modeled scene.
There are pages on my website describing starting operations on a small layout. In those pages, I describe how one can designate a section of a layout as "staging", even if it wasn't originally designed that way. In the case of your track plan, there's not as obvious a section to designate as staging.
I guess one question would be, how much are you wiling to rebuild to create the potential for more engaging operations and/or, how much can you add to the existing benchwork for new trackage (if you even care to)? You ask about connecting the stub-end of the yard to the rest of the layout and that doesn't seem very possible without major rework and/or additional benchwork.
Another question would be, what kind of operations interest you? You may not yet be able to answer that question if you haven't had a lot of exposure to other operating layouts, of course.
With the current plan, one way to approach it would be to treat part of your yard as the "interchange" yard with an unseen railroad imagined to connect at the stub end of your tracks. Cars placed on the two longest tracks could be imagined to be routed from- and to the other railroad. Then "your" railroad builds a train on the remaining yard tracks to serve your customers. That train rolls out on the line, picking up outbounds and setting out cars from the interchange yard. Then your train runs back to the yard, placing the picked-up cars on the interchange tracks for imagined delivery to the larger railroad. This constitutes one "operating session".
Between "sessions", you can manually swap the cars on the interchange tracks with new cars to simulate pick-up and delivery by the connecting railroad. Then the whole cycle begins again.
You can do a few things to add variety and a little challenge. Some passenger service can add some spice and add the challenge for your freight train of getting out of the passenger train's way. This could be as simple as a single Rail Diesel Car or as involved as a small "tourist" train operation operating older equipment. You'll have to figure out where the freight train can safely duck out of the way between crossovers as the passenger train runs, making a couple of station stops along the way.
In this way, you could at least get some operation out of your current plan while you learn more about ops and, most importantly, develop your own opinions of what will constitute engaging operation for you. Then you may decide to substantially rework or expand your layout.
If I were you, I would not give up on Koester's book. I think if you spend more time with it you will begin to see the overall picture. It's really not aimed at an especially advanced audience, but a few of the concepts require a different way of thinking. John Armstrong's book is excellent and you will be rewarded if you invest the time to really study it.
In addition to these resources (and the V&O book recommended earlier), I highly recommend the Operations Special Interest Group. Membership can be very inexpensive if you choose on-line delivery of the magazine. While it may take a while to grasp all of the concepts in the magazine, the OpSIG also offers a benefit to members of connecting them with operating sessions on various layouts either in your area or at meetings and conventions. In the end, the very best way to learn what model railroad operation is about is to do it.
Best of luck!