Through the years, I would guess at what I thought was the correct answer. 

1. 划线部分是 at 的宾语从句。what I thought 是从句的主语。

2. 这样的表达，英语太多，不用讲理论和结构，你可以联想：

What he said was a fact.

What I know is this.

3. 此外，这里 would 表示“过去的习惯动作”（意为：过去一直；过去常常；过去总是），不是“过去将来时”。例如：

She would often take a walk on campus when she was at univisersity.

她上大学时经常在校园里散步。

Mum would tell us stories before we went to bed.

过去，妈妈在我们上床睡觉前总是给我们讲故事。

Through the years, I would guess at what I thought was the correct answer. 

【直译】这么多年来，我一直在猜想我认为的东西是不是正确答案。