I don’t have any system per se… I just try to pay attention to every hand, including ones that I’m not involved in.
At one point some years ago in my home game (which started more than a decade ago) I actually wrote out a profile of each regular player for myself. Kind of silly, but the exercise forced me to clarify what I knew, thought I knew, or was unsure about their play. Typing it out made it a lot clearer and harder to go with just basic hunches. Then I knew going forward what I wanted to watch for each person.
Things which stick out as unusually bad are obviously more memorable... Guy opens from under the gun, calls a reraise pre and flop/turn bets, had nothing except a gutshot until the river, makes only bottom pair with 95o, then calls someone who obviously was strong from the start… What?)
In addition to basic stuff (like are they positionally aware, do they ever bluff, do they ever 3bet pre except with ultrapremiums, do they ever squeeze, etc.), I try to look for things such as what does it mean when this player overbets? Or, when they donk bet small, are they trying to set their own price on a draw, or is that what they do when slowplaying? Do they mix things up at all? Are they only getting to the river with top pair or better? Can they release a pocket pair that looks obviously beat?
Also helpful on the most fundamental level to know who just plays their own cards and who thinks (at least a little) about your image. What do they think when you bet buy? Do they assume you are weak when you check, and bet into it with air/weak made hands? etc.
The beauty of a regular home game is that you don’t really need to be in a rush to develop reads/profiles. Just pay attention to hands, think them through backwards when you have the chance in game, or afterward (as others have suggested). But mainly just let your observations accumulate.