Reflect will reduce damage taken from physical attacks for 5 turns; Light Screen will reduce damage taken from special attacks for 5 turns.
The effects of Reflect and Light Screen can be extended to 8 turns instead of 5 if the Pokemon that uses Reflect and/or Light Screen is holding Light Clay.
Reflect & Light Screen affect your entire team, not just the Pokemon that set up those screens (Pokemon that know Reflect & Light Screen are commonly called Dual Screeners).
Since both screens are set up on your side of the team, your opponent's Pokemon stats remain the same; essentially, the defences of your team has gone up temporarily, not the attacks of your opponent's team goes down temporarily. This means that any Pokemon your opponent uses will do reduced damage when the screens are up, except for Pokemon with the ability Infiltrator, which allows them to bypass the effects of both Screens, Safeguard and Mist.
Your opponent will do normal damage once Reflect and Light Screen wear off (after 5 turns or 8 turns if holding Light Clay).