First HOT 100, Aug 04, 1958 in Billboard

Chatfan MA wrote: Does anybody know if there was an introduction article in the Aug 04 issue or probably one or two weeks before (Jul 28 or 21) with more background on the chart's methodology etc.?

Yes, an article on the new Hot 100 chart can be found on page 2 of the Billboard issue dated August 4, 1958. As for the methodology, the article states the following:

In The Hot 100, data is obtained and tabulated right up to deadline time. Weighted factors in the carefully designed formula include disk jockey plays, juke box activity and sales at the retail level.

And that's all the detail they mention about how the charts are actually compiled.

Edited by Paul Haney

Thnx! Nowadays its the same, probably the delay is much
more. From Wikipedia:
A new chart is compiled and officially released to the
public by Billboard on Tuesdays. Example:

Friday, January 1 – sales tracking-week begins, streaming
tracking-week begins
Monday, January 4 – airplay tracking-week begins
Thursday, January 7 – sales tracking-week ends, streaming
tracking-week ends
Sunday, January 10 – airplay tracking-week ends
Tuesday, January 12 – new chart released, with issue
post-dated Saturday, January 23

I agree, assumed that e.g.the term (as shown in Billboard
Online) "The Week of March 12, 2016" really means the
week ENDING March 12 (thus the week of March 06 - 12).

Then the chart contains popularity of hits during a 10
days period from February 19 - 28 (sales, streaming and
airplay tracking).

Pre-announcement of the brand-new TOP 10 is Monday
February 29.

Online chart is published on Tuesday March 01.

Available as printed magazine on Friday March 04.

Looking on it that way the chart is rapidly available
within 1-2 days after closing date of data collection.