When you have a game up on the screen, to the right of the board you have several options as a diamond player. One of those options is "Explore". Click on the explore option and your current game comes up. It will give you a variety of optional moves (logical moves) or you can make your own. It will then give logical moves for your opponent. This option, of course will not be very usful if you are playing a blitz or bullet game due to time limitations. All of the suggested moves are based on previously played games, their frequency of use, and so on.
How do you plan out moves ahead of time?

You have to put yourself in the opponents shoes and think "What move would I hate him to play !"
Long term after you recognise mate in one, two etc obvious tactics, you then start considering pawn majorities, weak kingside structure and other strategic motifs...This comes with time...There's an undefined border where strategy meets tactics...
The question is a good one you ask and I'm surprised isn't asked more often..

Well, it depends...
If you are playing online, you can use the very helpful analyze tool. It allows you to make your move, and look at what the opponent can do, and if you should care...
If you are playing OTB, as long as you aren't using a clock, you can analyze as much as you like in your head for as long as it takes. (Just don't take 2 hours on move 1.)
I know how to make a plan for my own side of the board but how do I think about my opponents moves as well? I mean I'm not high enough to play masters so any move could be made, not just logical ones. How do I make a plan of action and try to make my opponents during my planning faze when it could be an arbitrary one?
Is there a way to practice how to make your oppenents moves for them? Play a game by yourself and move both pieces maybe?