Roscoe,
There aren't any magazines that focus on muay thai as far as I know. There are boxing magazines, but these cover the sport from a spectators point of view and do not cover training issues, conditioning or sparring.
Buying a book on muay thai (and there are quite a few out there!) wouldn't do much justice in the way of teaching or demonstrating, because muay thai is not an impressive looking martial art and it is taught differently than the arts you have previously studied.
In karate for example, a typical workout is like this:
Come in. Bow.
you warm up, stretch get into your horse stance and practice reverse punches, spear hands and palm strikes, then switch over to your fighting stance and practice your front snap kick, round house kick, side kick.
Next you do kata for 15 minutes on your own or in unison with the class.
The last 20 minutes you spend doing self-defense; your training partner grabs your wrist, gets you in a bear hug or tries to punch you and you execute a choreographed set of techniques that you will do 1,000 of times until you develop speed & fluidity.
Finish with a cermonialized bow to instructor, then shake hands.
I am certainly no karate expert, but have spent 5 years in the traditional martial arts and still talk to my friends who practice.
In muay thai your typical workout is like this:
stretch/warm-up
The instructor sets the ring timer for 2-3 minute rounds.
You go through circuits. During your first 2 weeks, the coach might pull you aside to teach you the basics. Once you get those, you learn alot on your own by working with other fighters and trial/error.
shadow boxing/kicking 2 rounds
Punching/Kicking heavy pads held by partners 2 rounds
Light sparring/sparring drills 2 rounds
Jump rope 2 rounds
Punchout/Pyramid Kicking drills 2 rounds - By this time you'll have lost 2 pounds of sweat.
2-3 rounds of either pad work with the coach, light continuous sparring with the coach or experienced classmate or quick- contact sparring (depending on your experience)
Your coach will stop the class to do some group work, which is motivating, involves team work but also challenging. You might do calisthenics or partner excercises like the fire man's drill, situps with your legs pushed etc.
Class ends. You shake hands with your training partners/coach and wipe off your sweat.
Did I forget to mention sweat
?