If I am immune to a particular disease, whether because I’ve had it (German measles) or I’ve been innoculated against it (polio), can you tell by testing a blood sample that I’m immune?
Ah, good practice for my immunology final.
The answer is - sorta. You can take a blood sample and measure its antibody titer against some particular antigen. By reacting successive dilutions of your serum against the antigen and observing if it reacts with the antibody or not, you can estimate the approximate amount of antibody against that antigen in your blood. There’s a number of ways to determine if the antibody is reacting or not, but this is the general approach.
Note that just because you have a high titer to something, does not necessarily mean you’re immune to it. Measuring the titer just tells you if you reacted to the antigen, not if you successfully reacted to it. Every antigen is different, and while this is true for some, it may not be true for others. The ‘protected’ level of titer is probably different for every disease being tested for.
Oh, good, I’m always relieved when one of my questions doesn’t just get a simple “yes or no” answer. 
Thanks for the info – but one further question – what’s a “titer”? Is that a number or score of some sort – an arbitrary scale – or does it refer to something “real”?
“Titer” refers to the highest degree of dilution of serum before the amount of antibody in it is insufficient to properly react with the antigen. Let’s say that you take a blood sample, spin it down, and get the serum. You have a bunch of wells with a constant amount of antigen. You put undiluted serum in the first well (1:1) - success. You put a 1:10 dilution in the second well - success. You put a 1:15 dilution in the third well - failure. Your antibody titer is then 1:10, the last dilution that successfully reacted with the antigen. The more dilute the solution has to be before the antibody is insufficient to properly react with the antigen, the more antibody was in the original serum, and hence in the blood.
Ah. Thanks.
And good luck on your final!