How do you "meditate on" a saying or subject?

Probably the closest that Buddhism comes to what you described is koan practice. In that form of meditation, the meditator focuses on the "turning phrase" of the koan. For instance, in regards to Joshu's Dog, the practitioner simply repeats the word "mu" on every out breath. No discursive thought is made on that word. You simply repeat it in your mind as if you were actually saying it aloud. The difficulty here is that inevitably, discursive thought will arise - both about the koan and about things in general. As the mind drifts down these avenues, the practitioner must reapply it to that word. Eventually, the meditator will begin to notice certain things about that word; certain experiences will also arise. These are the things that are then presented to the teacher who will in turn decided if the student has penetrated into the meaning of that particular koan.

I would say it depends on the tradition you follow. In general, it probably means to focus your mind on the word, phrase, or feeling, to the exclusion of other mental phenomena.

Coming from the Mahasi Sayadaw tradition of vipassana meditation, we might read a scripture, and make a mental note "reading... reading..."

While reading, we may get a pleasant or frightened feeling as we learn something from the text, so we then make a mental note "happy... happy..." or "fear... fear..."

As we go back to reading, we might come across a passage that we don't fully understand. Then we can make a mental note "confused... confused..." and so on.

The example I have given may or may not be helpful, since in our tradition we only meditate on directly observable phenomena as categorized in the Satipatthana Sutta. Overall, if you don't have much experience with meditation in general, I would suggest to find a teacher, and learn what you can. After you have gained some experience with meditation, then applying the teachings in daily life will be a more intuitive and less confusing task.

As for Yoda, all that I get is confusion so I say to myself (mentally) "confused... confused..."

The idea of a "focal point" is somewhat misleading, in that it implies attempting to impose a permanent point of focus. Even within the phrase "focus on the breath" we see that this does not refer to some limited focal point, but rather an ever fluctuating process. To narrow this even further, if we just look at it from a moment-to-moment relation, at the so-called in-breath/out-breath as it happens. What we see is that the in-breath itself cannot be pin pointed, nor can the out-breath. In other words, there is no-point of focus to be found!

The terms "focus" and "concentration" can be easily misappropriated as implying "to gain control". So, the phrase "focal point" can also be misappropriated as implying "to gain control of a specific object";ie. to gain control of thoughts, awareness, breathing, etc. Probably the most common mistake in practice is when it is motivated by a "gaining-idea"!! For most students/practitioners this is also the most difficult aspect of meditation practice to understand and overcome. That there is no-thing to be gained, no-point, no-reason, no-purpose, etc. to be found in the practice.

To simply "just sit" and nothing more! To do so without attributing any reason, purpose, etc., and without conjecture, explanation, expectation, or any other storyline/narrative as to why we do it, why it's important, or what we gain or lose as a result! So, in regards to words, phrases, etc., as a focal point, it is simply a matter of curiosity, contemplation, examination, etc., without any ulterior motives, or expectations of gaining. It's not a matter of some specific focal point, but rather of simply paying attention to the breath, to thoughts, to the inconsistency of focus itself, and to the limitations of our influence. And rather than picking one particular word, phrase, etc., as an object of focus, we should just be open and curious in general, and respond intuitively with the appropriate question. What is this? Where did it come from? Does this have some origin? Who is asking? Who wants to know? Etc...

Well, you should challenge what it means; both to you, and as general conventional term.

You should challenge that there is such a thing, and that anything at all possesses any inherent meaning. You should challenge this desire for certainty, this desire to make speculative assumptions about any and all phenomena, to attempt to isolate them, attribute definitive labels and meanings to them, categorize, and pin things down. You should challenge that there is anything at all to be gained or lost, to become or annihilate, etc.

What is love? Does it actually exist beyond these four letters which are aligned in a specific order and designated to a particular concept? If it does, then how? As a feeling? What is a feeling beyond the concept of it? Etc.. Etc.

The point is to deconstruct our own preconceived notions, and challenge our certainties. Because the essence of things is not found through speculative assumptions mistaken as certainties, or imposed meanings mistaken as the essence.

If we expect meditation to be some sort of tool for 'gaining this' or 'losing that', we will inevitability be disappointed by these expectations.

So, if we engage in meditation with the expectation of 'attaining/gaining' some sort of understanding or certainty, or 'avoiding/losing' pain and discomfort, this is a mistake. Meditation is a tool for recognition only. Simply recognizing everything as it is, that is liberation.

Shunryu Suzuki Roshi said something like:

"When you see something, then you intellectualize it. Then it is no longer what you saw."

To intellectualize things is to project a conceptual shadow over reality. We mistake these conceptualized forms, these shadows for being real. Then we chase them like kittens because we think that they can be captured and pinned down. And despite the futility of this, we continue to chase them every chance we get.

During meditation we just watch these shadows dance around without chasing them. And whenever we find ourselves being tempted to chase them, or if we have already begun to chase them, we simply return our attention to the breath.

So, it is this balance between "chasing"; deep contemplation, curiosity, challenging preconceived notions and biases, and "not chasing”; returning our attention to the breath, simple awareness as it is.

I hope that this is of some benefit and helps to encourage your practice :)

The breath is one of forty meditation objects according to the Visuddhimagga. For the full detail, see here, for a brief summary, see here