How to think during chess
I'm not saying that i've got thinking down to a fine art but I think I can help. When it comes to anticipating other players' moves I find because I've played the same opening, that has allowed me to learn what to expect due to experience, so learning an opening and sticking with it, I imagine, will help you see a similar position for hundreds of games.
However, if you want something more universal, Asking yourself important questions will help. The question "why did my opponent just move that piece?" and "How did moving this piece change the overall board?" Chess is generally about seeing ahead because all the information is already presented. By asking yourself these questions you are actively thinking about what your opponent is trying to do. If you can see what your opponent is trying to do then you can attempt to counter it. Asking questions after every single move may stop you being blindsided by incredible moves from your opponent. Not only this but it may also help you find mistakes and blunders from your opponent since in a position you may realise its not a good move because of x reason and you can capitalise on this mistake.
Additionally, missing tactics of your opponent can equally be down to not recognising that they are tactics. There are 5 free puzzles per day on chess.com. I'd recommend doing as many as you can a day and take as much time as you need until you are certain you have the answer, don't worry about the points to start off with. This will improve your calculation and pattern recognition skills which are important in chess.
Good luck and welcome to chess.
Experience helps. But doing tactical puzzles sppeds it up, since you start to understand that seemingly an ordinary position is hidding an interesting combo that suddenly wins. You don't even need to recall all the time that you should slow down and check for checks, captures and threats - eventually it happens by itself when seeing so many tactical situations.