Saving in game is usually saving the game progress that is by saving the variable values to a local file. first you have to think of variables that is showing the progress. Usually position of character, Score, money or similar, Health, no of lives, current mission detail or similar. This variables depends on the game you are making.
Do basically instead of giving certain constant value to the variables in start or awake, you have to read the values from local file or server or what ever other means you are using for data back up and set that values to those variables.
In unity you dont have to do much to save the gamedata or retrive it. There is several ways to save , but the easiest one is using playerprefs. Look in to that class you will understand it pretty easily.
If you dont want to use player prefs you can always serialize the whole class and save its object as a byte array in to a local file. you can use stream reader and stream writer or any similar stream handler class for this process. It is a bit more complicated but you will have a good access over your data.