Wondering how sound, videos, and
png work in fasm. ogg sound, ogv video, png, and bmp.

Work in what way? Do you mean the file format? fasm doesn't specifically deal with any media formats but you can write code (for fasm to assemble) to decode and play/display media content in your chosen OS.

How would decoding it work? Do I study the formats source code?

If it was me I would start with reading the file format specs. Probably only when all else fails would you want to read some source code to extract the algorithms and file layouts.

Thank you Dr.Revolution.

You'll have to research the file format (media format in this case) then interpret/translate the algorithm into assembler essentially creating more commonly a decoder. Ogg and mp4 files (as examples) are read using decoders then output in the native format (Ogg or mp4 in this case) or transcoded and output. Transcoding is generally unnecessary except in situations where media is streamed to a device that does not or cannot support the original format/algorithm.

Regardless, you will have to do background research on the format optionally getting pre-existing examples (generally in C and/or C++) then develop your assembler media development libraries from there. You could also investigate using third party libraries in the desired operating system by including the DLL/SO executables instead of writing your own.