How do we know if an odd number is the sum of two primes? is it always through trial and error?

Hint: primes are odd with one exception. What does that do to your answer?

2 is the exception. Does that mean if you add 2 to any prime number it results in an odd number because even + odd (all primes besides 2) = odd?

so for e.g. 99 =2+97 so 99 is a sum of two primes if 97 is a prime?

Indeed.