Crypto papers actually kind of suck; my experience is that roughly 2/3rds of the time, the complicated formula on the page works out to a "for" loop that would be trivially easy to understand if expressed in algol syntax.
Best advice: do deep research on TLS. For every feature, do a directed search of the literature and do experimentation to try to figure out why that feature is there. Most of the features in TLS exist as a countermeasure to some attack. Follow this tack all the way down the stack, starting with the high-level protocol features and working your way all the way down through the block cipher modes and configuration that it uses.
Yeah there definitely is a bit of an art to reading them. But we can't have cryptographers and security professionals merging too fast... that would just make too much sense. :P
Best advice: do deep research on TLS. For every feature, do a directed search of the literature and do experimentation to try to figure out why that feature is there. Most of the features in TLS exist as a countermeasure to some attack. Follow this tack all the way down the stack, starting with the high-level protocol features and working your way all the way down through the block cipher modes and configuration that it uses.