The problem with trying to convince people to try meditation is that it's a very "darmok" type of conversation, it's like trying to explain purple to someone who is color blind. Meditation is one of the most complex and subtle and yet also one of the most simple things imaginable, it's very difficult to accurately sum-up everything going on with it not only in a succinct way but in a way that is completely understandable to people who have no experience with it. I'll give it a shot nevertheless.
First off, understand that the way skills of the mind work are like any other skills. The more you practice, the better you will become at them, and the more conscious control you will have over them. Think about something like throwing a baseball. It takes a lot of practice to get good at it, but eventually you do get better. And then you set up "hooks" from your conscious mind (certain triggers in the way you hold the ball and stand, etc.) that bridge the connection to the unconscious hand/eye coordination parts of your mind. Something similar can happen with purely mental things as well. You can use classic training techniques (stimulus/response etc.) to train just about anything you want, though in practice it's been discovered that a few specific kinds of skills are more important than others.
Think of it this way. Do you have any activities you do to relax? Do you have any comfort foods? Do you have a favorite shirt or piece of clothing that boosts your confidence? Do you have any phobias or fears? Do you have any pet-peeves (like bad drivers on the road)? All of those things are actually learned behaviors. But all of them are based on external, physical triggers. Maybe your response to eating your comfort food was built up over years of being raised in a loving household and a particular food item reminds you of that. And then eating that comfort food later also reinforces its place as a comfort food because you will have previously used it for comforting and found it to work. Have you ever watched a storyline on television or in the movies where someone has been given something like a drug or a lucky talisman or something and gone on to be successful and confident with some activity only to discover that they were tricked by their friend who gave them the thing and in actuality it was a placebo, and the confidence/talent was in themselves all along? Meditation is the same way. Imagine having a lucky shirt that makes you feel more confident when you wear it. But then imagine spending a lot of time practicing pretending you're wearing the lucky shirt whenever you want to, giving you the ability to have that "lucky shirt" feeling whenever you want to. Think about all of the other ways people try to influence their own mental state through external behaviors (going on walks or drives, taking a bath, taking a vacation to get out of a rut, listening to music, etc.) and imagine if you could go into the brain and, say, "going on a long drive in the country" with just a lever that you had control of. Everyone already engages in these sorts of behaviors to change their own mental state, they just start with external methods of triggering those changes.
So that's one aspect of it, but it's hardly all of it. Brains are complicated machinery, and mastering them is equally complicated, and subtle. Another major aspect is mindfulness and "being mode". It's very easy for humans to get stuck in "doing mode", so much so that people tend to think of it as synonymous with existence. Doing mode is how your brain gets shit done, and it can be very effective. It has to be, because it was evolved in an era when not being able to complete objectives could translate to death from a million different potential sources. Doing mode is like a PID controller, it's constantly examining the separation between the desired state and the actual state, and driving towards lessening the gap in every way possible. It's great if you're trying to escape a leopard or avoid starvation, but it has some negative consequences in our modern world where the things that your brain might think about wanting to get done are not exactly easy to get accomplished within a few minutes. Indeed, the brain's "doing mode" mechanisms are the source of a lot of unnecessary rumination and negative self-talk which cause or greatly enhance a lot of unhelpful mental problems like depression and anxiety. Moreover, doing mode has tunnel vision. It is a furious optimizer and will constrain your experience of the world down to the essentials for getting something done. If you've ever done something on "autopilot", had to re-read a section of a book several times, or done something like scarfed down a meal while multi-tasking with something else, you know what this is about.
Unfortunately, these traits cause doing mode to often burden us with anxieties, depression, and a diminished level of perception of the world. The most direct cure for the excesses of doing mode is to learn "being mode" or mindfulness. In being mode you learn that thoughts are just thoughts, they aren't "you" intrinsically nor are they inescapable. You learn to reconnect with your senses and your experiences as they happen. This can have a profound impact on life because being able to acknowledge a thought in your head, say to yourself "this is a thought, but it's just a thought, I can think it or not, but it's not necessarily me, nor is it inescapable" can rob a stream of negative self-talk (in anxiety or depression) of its power. And experiencing the world mindfully in the moment is almost inevitably a way to improve your happiness. This is very much a "stop to smell the roses" sort of thing, but in a "you're already smelling the roses, just connect with that experience and actually allow yourself to experience smelling them" sort of way.
A lot of mindfulness is based on acceptance and compassion, which are cornerstones to how the whole system works. It's not about forcing yourself to "get better" at some skill. It's about putting out feelers to connect with your experiences, finding what's there, carefully and compassionately acknowledging what's there, and moving on. You don't have to force yourself to do or think anything special, but by engaging in practices regularly you'll often see changes regardless. Accepting is about accepting the good and the bad, experiencing it, and being sufficiently mindful to let it pass through you rather than control you. Often these practices have a strong positive impact on people, but the irony is that if you try to force that sort of control right out of the gate you'll often fail.
It can be unbelievably powerful though. I've had times of having very serious negative thoughts that might push me into a bad mood spiral come bubbling up and experienced moments where I simply acknowledged the thoughts as just thoughts and then watched (mentally) from the sidelines as those thoughts were robbed of all power and just dissipated instead of drowning me in sadness. I almost cried experiencing that for the first time.
So much of mindfulness and meditation is about shifting your perspective with respect to your body, your mind, your self, your feelings, and the world. Through practice you build up skills in taking more control over your mind, because in a lot of ways those skills have to be built up subtly, without necessarily directly aiming for them. One of the big ones is just basic breathing meditation where you sit, concentrate on your breathing and basically watch as your thoughts go by. Is the point to have no thoughts? No. Is the point to have only very specific thoughts? Not really? Is the point to beat yourself up if your mind wanders? Quite the opposite. But the thing is, if you sit and just do that on a regular basis you're going to get better at watching thoughts go by in your mind, and ironically you'll end up having more control over that process. Think of what happens when you're trying to concentrate on a task? You get distracted by other thoughts and stimuli (also thoughts). Imagine if you'd spent a lot of time practicing just watching thoughts pass by without letting them hook you and take you away. Think you'd be better at concentrating?
If you want to try meditation / mindfulness with minimal effort just set aside a few minutes every once in a while and spend some time where the only thing you're consciously doing is breathing and being a spectator for your own thoughts, watching them go by, discovering when you've become distracted by one and simply acknowledging the inevitability of that happening before returning to your brief period of thought-watching.
The end result isn't turning into a Jedi or a Wizard or developing a special power. It's being able to connect with yourself, increase compassion and understanding of yourself, and to be able to be in the moment and present in your own life, experiencing it with fullness and richness (the good and the bad) without being shunted off to autopilot all the time, and being able to not be subject to the whims of your own self-criticality.