White Light Interferometry I have arrived at a way to produce Arago’s spot with a quality white led flashlight. 

How would I go about writing a small educational paper on this? 

And, most of what I have seen on the web uses lasers with very unspectacular results.
 A: Welcome to physics.SE!
Your questions seems to be a bit off-topic, as it rather deals with writing or even publishing than actual physics, if I am not mistaken. However, I will quickly sum up how to write a short report, as I assume this is what you have in mind.
Usually your paper will be structured as follows:


*

*Abstract: You state the problem you solved, the technique you used and the result you got in a couple of sentence, ideally no more than half a page, but 5 lines is fine as well!

*Introduction to the topic: On what grounds did you start, which knowledge is assumed, why is your result important.

*Experimental set-up: What did you use? The equipment, the procedures, the methods, maybe the formulas you used, if you calculated things.

*Explain the experiment you undertook, step-by-step, so that it is reproducible.

*Present the results, measurements.

*Discuss your results, compare them to literature / papers, point out possible shortcomings of your work and explain why these are negligible (if so, otherwise: why didn't you do it differently then?!)


Make sure you cite every external sources you used. Be clear about your methodology, how did you do things?
If you want to publish it look for journals that are appropriate, according to your level or rather on the level of your experiment. If you wrote your article on overleaf you can directly upload it to publishers. You can also consider to just have it online, maybe as a web-page, a blog post or as an article on arXive. Having it on researchgate would be another idea, you could share and discuss it there.
I hope this answer goes into the right direction and I wish you good luck with your project!
