If you do a google on "tephigram" you get several pages explaining how to interpret them.
There is a lot of additional information to be gleaned from the various lapse rates but I never got that far
A few weeks ago I posted a rough guide to determining the type of cloud to be found at various levels, according to how close the temp and DP get. My knowledge on this is only basic.
Not many pilots know this stuff, which is a shame. Unfortunately, absolutely everybody I have ever come across who understands this kind of advanced aviation weather (upper atmosphere met, basically) is either working for the UK Met Office, or is involved in one or another commercial weather data repackaging company.
If you want to learn it, it may be an idea to book a day with certain people I can give you details of, and bring a few friends to spread the cost.
The key thing is that it needs to be learnt in the practical context i.e. getting the data off the internet.