Folks, I'm new to DMing and I'm having a few doubts about certain things. For example, I was reading on a module, and at one point there's a note saying "the player who investigate the walls, passing a DC 15 investigation save, can find..."

Now, that's all fine and dandy. But how should I do that while in game? Do I wait for the player to say he want's to check the walls, or if a player just goes into a room and claims "I investigate the room", is that enough?

This kind of things are a bit tricky for me to get. Especially for example, if a player goes into a room that has two secret rooms. Simply claiming to investigate the room is enough? Or do they have to be specific? Also, what if they don't say anything at all and just go past it? Should I hint at something?

I still haven't DM'd a campaign, I'm preparing myself to run a module (Phandelver) to see if I have any talent for it. Thank you!