Is there any way to have users enter a unique ID number in a column in list A, have it reference list B (which contains data about them) to pull their information such as name, city, state, etc...? This would then populate columns in list A with the corresponding fields.
If I understood your question correctly. You need to create a lookup column in list B and refer it with the column from list A(in your case you need to refer ID from list A). While creating lookup column, you can choose what information you want to present from List A.
Here is an example: Link