Plug a SNES or a PlayStation into a modern television and the picture can look soft, laggy or downright wrong. That is not the console failing — it is a mismatch between an old analogue signal and a screen built for crisp digital input.
The first cheap win is a better cable. A composite (yellow) lead is the bare minimum; RGB SCART or component leads carry a much cleaner signal and the difference is obvious the moment you switch. For consoles that support it, this alone transforms the image.
The second is input lag. Many tellies add processing that delays the picture, which is fine for films but ruins anything that needs timing. Dig into the picture menu and switch on Game Mode — it strips out that delay and makes the pad feel responsive again.
If you are chasing a truly sharp result, a dedicated upscaler sits between console and TV and does the conversion properly. It is the enthusiast option, but for most people a decent cable and Game Mode gets you 90% of the way for a few pounds.