You can save as often as you like, even in the middle of puzzles and conversations.

I strongly recommend that you change the name of your saved game each time you save so that you have more than one saved game. The game is designed with no dead ends, so you'll never have to go back and start over to get out of an impossible situation. All the same, you never know when your power is going to go out or your computer have a hiccup or something. You might also want to replay a specific part of the game to see what happens when you make a different choice.

I usually save my game with a name that says what I was doing at the time -- "Looking for Bess" or "End of day 1" or even "Stuck stuck stuck!"