To try this yourself you'll need a large-ish flat surface with parallel lines at regular intervals (same distances between them), and you'll need a needle or a straight stick. It helps to have someone else write down the results so you can do your trials more quickly.
Drop the needle onto the lined surface so that it falls "randomly", and note whether it comes to rest on a line or not. You'll get more "randomness" if you drop from higher up or toss the needle haphazardly.
Once you have done at least 100 trials, the formula for approximating Pi is... (twice the number of trials)/(number of times the needle crossed a line). The more trials you do, the better your approximation will be!
My only question is... What do I eat on approximately π day?!? Apple crisp?
(picture in public domain, from wikipedia)