Create a new class inheriting from TileBase (or any useful sub-classes of TileBase, like Tile). Override any required methods for your new Tile class. The following are the usual methods you would override:
RefreshTile determines which Tiles in the vicinity are updated when this Tile is added to the Tilemap.GetTileData determines what the Tile looks like on the Tilemap.Create instances of your new class using ScriptableObject.CreateInstance<YOUR_TILE_CLASS>(). You may convert this new instance to an Asset in the Editor in order to use it repeatedly by calling AssetDatabase.CreateAsset().
You can also make a custom editor for your Tile. This works the same way as custom editors for scriptable objects.
Remember to save your project to ensure that your new Tile Assets are saved!