A simple way to do zazen is to sit, legs crossed if possible, back straight. Rest your hands in your lap. By all mean search formal zazen postures, but this will get you most of the way there. Then, simply relax and count breaths. In, one. Out, two. In, three, and so on. Count to ten then start again.
The object is not to block out thoughts or force your mind to be blank, but to let thoughts go as easily they come, and notice the still moments in between. If you notice stillness, slow your counting to only the in breaths. In, one, out. In, two, out.
With practice, there will be fewer, briefer thoughts, and more stillness. Do it for 2 minutes. Then 10. Try every day, see how you go. If it works for you, perhaps try 20 or even 30 minutes. Perhaps consider finding a group. Sitting with others, even if only online, makes both the sitting and the stillness easier, somehow.