There are many kinds of meditation, and as many ways of explaining them as there are people. After years of study and practice, here is a meditation I recommend. I call this "the coming to one's senses meditation" :)
Sit any way you want, as long as it's not too uncomfortable nor too comfortable as to put you to sleep. You can change your posture any way you want. Don't worry about it at all.
Bring your attention in front of you. Not literally "in front", but rather "to the room". It is the same kind of attention you need when you were busy for too long and neglected your room, and now you are finally coming back to the present and taking a good look at your room - and noticing the overall disorder. It's a similar feeling to awakening. "Hiii, present moment! Long time no see! I was waaaay too busy lately." Finally the Sinbad is back from yet another travel. This is why it's called "coming to one's senses".
Look at your body. Look at your hands. Feel them. If you are like most people, it's been long time since you gave attention to your basic being. Feel your entire body, as presence, as energy. It feels so good to finally stop running like a hamster in the wheel and come back to one's body and one's room. At the same time, you may have a feeling of anxiety. It feels like you are wasting time doing nothing. You've been running on for too long, and it became a habit. Feel that anxiety in your body. Drop it. It's okay to waste time. In fact, this is a precious way to use time, you are reconnecting with your basic being.
Don't worry about the clock. If you do do worry, put a timer for 15-20 minutes, and test it first - it will help you relax knowing you won't "waste" too much time ;) So in this case the purpose of the timer is the opposite of normal. You use the timer for its silence, not for its alarm. If you do trust yourself and don't worry about time - then you don't need a timer.
Come back to your senses. You've been driven for too long by all those goals and problems, now is time to gather your thoughts. It's a same feeling like you are on vacation, or actually it's like you added several days after vacation, to stay home and gather your thoughts. That's it! So you sit and you're like "pheew!" Finally. It's that state of mind when you can finally think "Alright, what should I do next?". You are reconnecting with your inner core and sending a silent SQL query to your guts: "give me the top 5 things I wanted to get to but never had time".
Now, this moment is when there is departure between meditation and regular thinking-and-gathering-your-thoughts type of sitting. Normally, you get absorbed into the first of those 5 things, or maybe the second one - and go on creating new plans, and that's it, vacation is over. Instead, with meditation, you stay in that query mode, and let your guts keep on finding more and more things that you have been previously deferring. Remember those old stories about a student tasked with reciting prayers in a church all night long, while all kinds of horror creatures come up but the student should keep his cool? They are the echo of this meditation.
The trick is to stay fully present in the room, just like you were in the beginning. Maybe 65% of your CPU is staying in the room and feeling the presence of the body & the freshness of the current moment, 20% is running the deep query, and 15% is the control circuit ("you") aka mindfulness. The role of the control circuit is to gently restore the balance when it skews too much towards thinking. Meaning, when the query comes up with a result, your role is to take it, bring it fully into your present moment, and take one good look at it while keeping at arms length. Then gently dismiss it, while leaning fully on the visual awareness of your presence in the room and the feeling of aliveness of your body. Don't rush to do anything at this moment. Wait until your mind fully comes back to the room and the initial "gathering your thoughts / what should I do next" state is restored. This is the critical moment! Don't rush into the next cycle. Let yourself waste time! When you get present and stable enough, your body will automatically send the next query to your subconscious. Don't think about it at all, just come back to the initial state. That's it! -- Repeat like this until you feel super-awake. I call this process "thought laundry" or "mind washing machine". This is the vipassana element.
You don't have to obsess with the laundry cycle either. Sometimes you may feel like not waiting for query results at all, and focusing on your overall inner comfort instead. This is also a valid mode of "coming to one's senses meditation". Perhaps you feel like your body was crumbled and now you want to open it up. Perhaps you feel like your aura was burning with anxiety and now you would like to apply the metaphorical aloe of contentment. Sometimes you may feel like you want to uphold a kingly posture or stretch the face muscles or open the chest etc. As long as you don't go too far into the sport exercises, and your main activity remains sitting in the room, gathering your thoughts, and coming back to your senses -- all kinds of psychosomatic comfort motions are very valid. May be you'll realize you've been drowsy all this time and you want to make an effort to awaken your mind. All these are good. I call this "conditioning the mind". This is the samatha element.
The most important point is: it's not about doing anything. It is about coming back to your senses. Both conditioning the mind as well as coming up of the deferred thoughts are just aspects of coming back to your senses.
So as you see, in this version, it's not really thinking, nor is it no-thinking. It's not mindfulness of any one thing, but it's not no-mindfulness either. It's coming back to one's senses. If you do it right it should be quite enjoyable! Although every time you still need to overcome the tendency to continue worrying about the things that worried you that day or the previous day. Also, on some days you may have trouble doing this at all, if thoughts or emotions are too strong. In that case, don't need to force yourself. When you force it, your heart will start hating it - and then you won't do it at all. But if you're doing it right, it feels like finally finding time for your most precious friend. Over time you should be able to extend the sitting from 15-20 mins to maybe 40 mins. Maybe in the future you will want to sit for 2 hours, like the monks do. Maybe one time you will be encouraged to sit for entire weekend, with only snack and bathroom breaks - who knows.
But even if you only do it 15 minutes a day, you should feel much more stable and awaken throughout the day. It works like sleeping, just 10 times more efficient.