My understanding at a high level is that an IQ test is basically made by generating a bunch of cognitive tasks that putatively test different aspects of cognitive functioning (e.g. verbal reasoning, visuospatial reasoning, attention, working memory, etc.). For most people, performance on one type of cognitive task (e.g. verbal reasoning) is highly correlated with performance on the other types of cognitive tasks.

This allows you to model the test as a hierarchical statistical model with some general intelligence factor (denoted G) at the top and then specific cognitive tasks branch off from there. You can then infer what G is just by statistical inference on the "branches" (the performance on the individual cognitive tasks); similar to how you might infer someone's height if you only had access to their leg and arm lengths, as these are highly correlated with each other and also with height.

I believe IQ scores are always population normed to have a mean of 100 but unnormalized scores are likely available to compare across time.