Write the numbers 2 to 100 in a grid. Circle 2, then cross out every other multiple of 2. Circle 3, cross out multiples of 3. Repeat with 5 and 7. Whatever survives is prime.
Why only up to 7?
If a number under 100 isn't divisible by 2, 3, 5, or 7, it can't be divisible by anything else either — because the smallest factor of a non-prime is at most √n.
Eratosthenes invented this method around 240 BC. It still works exactly the same today.