Again, I'm new to biology and have a bunch of questions. Does it depend on the proteins involved? OR are there basic co expression procedures one could implement to determine exactly how much one protein upregulation leads to overexpression of another protein ?
To demonstrate a causal relationship where protein A leads to increase in protein B, you need to experimentally increase the level of A and measure if B increases. Over-expression is typically done with overexpression of protein A from a plasmid containing the coding sequence, driven by a strong promoter that causes high levels of protein synthesis. See this Wikipedia page for some pointers. Relative protein levels can be quantified by western blotting. The experimental details depend a lot on what cell type and protein you are studying, of course.