So you can learn about the rock-paper-scissors formula either by trial and error or in talking to some NPCs. I think the guy just inside each gym will also give you tips.
However it's worth noting that Generation 1 (like Pokemon Red) has a number of unintentional bugs programmed into it. As a result Psychic type Pokemon are extra powerful. If you can get one of those, you'll be in good shape.
Additionally, some of the early game can be difficult to figure out. For example if you picked Charmander as your starter, you might be OK with Viridian Forest, but the first two gyms and related battles will be much more difficult.
Gen 1 is also missing A LOT of quality of life improvements. If you can, I recommend Pokemon Fire Red (or Leaf Green). It's the remake of Gen 1 and it's for the Gameboy Advance.