A great Halacha Parsha Inyan Magen Avrhom, Aruch HAshulchan,Chazon Ish. Feeding the Birds on Shabbos Shira Minhag shtus or Minhag Yisroel Torah.I don't know what I can really add to it. It concisely summarizes the inyan, with various relevant marei mekomos. You can read about it at length in What Is Bothering Rashi, on parashat Beshalach. Also, this footnote in an article by Rabbi Dr. Ari Zivitovsky:
As well as many other places on the web. This, for example, is a good writeup on plausible midrashic sparks for the custom. So what is there for me to do? One thing I might be able to do here is actually track down each of these sources and present them for reading, inside, rather than have people rely on summaries.
I'm not going to do this. However, briefly, here is the Aruch Hashulchan, Orach Chaim siman 324:3:
And that Magen Avraham, same siman:
Indeed, it may well illustrate overall approaches to halacha and Jewish practice, with Mishna Brura operating based on entirely technical analysis, and with Orach Hashulchan granting great credence to actual Jewish practice.