That was part of my commute for 6 years ... happy memories!!???
Kings X is a big station, with lots of potential for confusion ...
If you are arriving at Kings X on the Piccaddilly/Northern/Victoria lines, there is a long tunnel to get you over to the Thameslink station - 'just' follow the signs.
If you are arriving at Kings X on the Circle/Metropolitan lines or by national rail (at the mainline station), it's easier to walk out of the station up to street level and follow signs east along Pentonville Road - it's about a 5 mins walk.
You'll get there no problem - hey, if you need a break, there's a great little Greek Cypriot run cafe just past the Thameslink station on Pentonville Road!