training the mind to go to that place of calm management, and eventually being able to not quite turn off the unwanted thoughts but to shift the inner monologue
Personally, I found mindfulness (Headspace) helpful and accessible, and I've found that yoga gives me the same mental stability I got from the mindfulness
For meditation purposes, try not clearing your mind but just focusing on breathing. Endlessly counting your breath from 1 to 10 can be really useful, then forgive yourself every time you get lost and just start again.
In terms of judging try thinking about this: mistakes/errors don't exist, they are only a meaning we as humans have given to stuff that we dislike. In any situation, try figuring out how that situation is perfect for you at that moment, how could you have chosen that situation/moment ahead of time on purpose? It's not easy, but it's simple. How is everything in your life just perfect right now?
That said, also be aware that meditation isn't the panacea that it's often made out to be. It certainly sounds like it's what you are looking for at this moment, particularly since you mention that you 'can't meditate'.
It's not about shutting those thoughts up at all. It's about recognizing those thoughts as they begin to enter your mind and using the meditation as a tool to either embrace those thoughts (sometimes we need to) but recognizing they likely aren't our reality and are likely just thoughts from past experiences or future expectations. It's your reaction to those thoughts that is really important and a lot of us who don't meditate tend to ruminate on things that we know aren't beneficial to us. It helps you learn to control that better.
I'd recommend following guided meditations, I specifically enjoy metta (kindness) meditation. Your instructor will occasionally tell you to allow those thoughts in so that you can get better at recognizing them as what they are, just thoughts, not something you have to act upon or believe. Then they'll typically have to go back to focusing on your breath which will make those thoughts disappear, even if only for a short time.
It takes practice. Don't fault yourself for not being a meditation guru. Nobody is. Just be kind and accepting to yourself as it happens. There's no rush. Some of my meditation sessions are much worse than others, just like my workouts.
After a month of daily meditation (which I'm unfortunately not doing lately) I become such a calm person. I still get that twinge of anger when someone cuts me off or traffics bad but I notice it as soon as it starts to enter my mind and I can control my output FAR better. Usually I just go "oh, that happened, it's out of my control, what I can control is my reaction to it."
You are describing a completely normal frustration with intrusive thoughts and are being entirely too self critical.
It's very hard at the beginning, but if you persevere, you'll eventually get there.
Just remember the first time you were doing push-ups. It's like that. Like doing push-ups with your mind. Very hard at the start, feels great after you get used to it.
I’m not saying it will help, but not all approaches to meditation get the same result and this one might really address what you are experiencing.
I suggest you reframe the act of "meditating" as being the moment when you become conscious of yourself being distracted, and bring your mind back to the object of meditation (the current moment/breath/mantra, etc). Think of it not like work, but more like a game you're playing. You can even tell yourself, "aha - noticed I'm thinking rather than following the breath," etc.
In other words, successful meditation is all about your mind wandering, you noticing it wandering, and you bringing it back. The more you notice the attention wandering and the faster you get at returning it to centre the more "meditating" you're doing.
Holding your mind rigid is just going to make you frustrated.
Incidentally, over time, learning to notice your attention wandering ever more quickly and bringing it back more reliably will produce new mental states. And over time your mind will wander much less often. But this is all something that's achieved indirectly. If you aim directly for the mental state you'll find it much harder if not impossible to achieve.
Just sit.
"thoughts intrude"
Just sit.
"angry at myself"
Just sit.
"I give up"
Just sit.
Breath.
Just sit.
I recommend reading the book "Don't Shoot the Dog". It is about conditioning, but despite the book's name, most of the information applies to humans, too. It explains the details that matter, and how most people who try to use conditioning actually do it completely wrong.
One important insight is that using punishment to condition yourself almost always backfires. The reason is quite simple: every time you punish yourself for doing X, you are simultaneously conditioning yourself against two things: (1) doing X, and (2) noticing that you are doing X. If X is a bad habit, guess which one of these two things will be extinguished by conditioning first. And most people are already quite bad as self-understanding.
Therefore, perhaps the most important rule in meditation is to never punish yourself. (However, also don't punish yourself for breaking this rule. That would only mean breaking the rule twice.) Every time you punish yourself for "meditating incorrectly", you are going against what you are supposed to achieve by mediation. You are discouraging insight (to have made an error, that is a useful insight), and even discouraging meditation itself (the less you meditate, the fewer errors in meditation you can make).
In traditional Buddhist countries, beginners start with the loving-kindness meditation, and only later move to concentration exercises. Which is probably designed to avoid negative thoughts while practicing concentration. But many people in the West are likely to go straight to the concentration exercises, because they are looking forwards to increasing their productivity, and ignoring the loving-kindness meditation, because that's some stuff for hippies. And then they happily go and tell others to do the same. (Or course, a hippie who would only do the loving-kindness and never move on to concentration, would also be doing it wrong.)
The proper mindset for concentration meditation is unconditional self-love. You do it right, that's great! You do it wrong, hey, it's great that you noticed, and it's great that you keep trying regardless! Self-awareness and perseverance are wonderful traits, why would you ever punish yourself for having them?
Now the important thing is that you need to do this sincerely, not ironically (like, "I am such a loser, oh, good job noticing that, loser"). Self-deception would be the opposite of what you want to achieve. When I write that being self-aware (even of making mistakes) is preferable to not being self-aware (but making the same mistakes regardless), I totally mean it. But this attitude can be difficult to adopt, if you are not accustomed to having love expressed towards you (by others or by yourself). In that case, doing the loving-kindness meditation might help to overcome this obstacle.
I suppose that if you do meditation without punishing yourself, you will feel less exhausted. (Unless there are other reason, e.g. you were already exhausted, and mediation only helped you notice that better.)
tl;dr - to succeed at meditation, not being angry at yourself is more important than stopping your thoughts; you may want to train this skill separately
Having something else to focus on can help - chant a mantra (just "om" works okay if you don't wanna look for anything more Perfect For You), count your breathing and reset the count every time your inner voice interjects something or when you get to ten, stare at something (I like just staring at the grass sometimes and watching how my visual centers start acting when they get really bored with looking at it).
A big key is to stop being angry at yourself for failing to stop that internal monologue. It's a hard thing to do! Instead of beating yourself up, just shrug, forgive yourself for doing it (maybe even say "I forgive myself for failing to quiet my inner voice" out loud, this activates different parts of your brain), and go back to whatever you're doing to focus on next-to-nothing.
If you can block out the time, I found that my meditation skills got a lot better when I stopped trying to do it for a few minutes at a time and started setting a timer for thirty minutes. Some days I can stop thinking easily. Other times I keep on fighting it for like twenty minutes. But doing it for a long stretch like that gives you more chances for your twitchy brain to get bored and STFU.
It's much much less about just blanking out or how long you can maintain the focus and much much more about how you deal with all the craziness that your subconscious is doing to you. Minute by minute; each time it happens. Because it's not going to stop happening, during the exercise or not. Your mind is going to do what it wants; figuring out what you can do with that fact during the exercise then carries over to the rest of life.
I will add that it's taken me a long time to get to the point where I'm not frustrated with myself for getting distracted, so I'm not trying to say this is easy. On the contrary. But it's been worth it for me.
Meditation is not actually about being free from thought. The goal of meditation is actually to notice when attention wanders, thoughts come walking in and pull back to the breath. That's the muscle you're strengthening. Each time you notice an intrusive thought, is actually a moment when you're actively meditating.
The goal of meditation is not to succeed at being free of intruding thoughts. It is to practice noticing intruding thoughts and bringing your mind back to focus.
Having an intruding thought while meditating is not a failure any more than lowering a weight while exercising is a failure. You can’t lift if you don’t lower.