Resident Evil 2 uses a type of autosave system, but these are few and far between. You should definitely not rely too heavily on the autosaving, and if you want to play the game without a constant fear of loosing all your current progress, finding out how to save in Resident Evil 2 is important.
Like many survival games, you cannot just open the main menu and save any time you like. Instead what you need to do is to find a typewriter. These typewriters function like a save point, so interact with this typewriter to open up the save menu. This gives you the ability to save on one of several slots, and if you play on Standard or Assisted difficulty, you should save as often as you find a typewriter.
If you play on Hardcore difficulty, it get's a bit more tricky. However, here's how to save your game on hardcore difficulty in Resident Evil 2. Before you are able to interact with the typewriter, you need to find an item called Ink Ribbon. These consumable items are scattered all around the game, so you will need to just search boxes and keep your eyes open for them as you play the game. They are kind of rare, so don't expect to be able to save on every typewriter.
Saving in hardcore mode in Resident Evil 2 consumes 1 x Ink Ribbon, so you will need to constantly find more of them if you want to further save your progress. Anyway, that's how you save your game in Resident Evil. Good luck!