It only needs three lines of code. You can also simply click and a button to add it to your sidebar as a widget. If you want this Related Posts just right after your post, you only need to manually add these three lines of code at right place.
Honestly, I didn't write it with much care, so it might be broken very soon or never be. I don't know how many posts data can be stored within 500MB, I haven't written any clean-up code. The speed is quite fast, just a second or two for querying 5 labels via Blogger Data API. I may raise the label querying limit to 10 or higher, when BRPS has more bloggers use it.
The JavaScript script is relative simple, but enough for bloggers use standard templates. I am very welcome anyone to improve it or any part of BRPS.
Again, I am a lazy person. Current status is all what I need, I will only fix bugs for myself. I wish you can request some features, then I will add them if possible.
Updated on 2008-11-17: Here is a link to a blog post, which collects the old ways.