[HunterM]

"trainieren", as mentioned, doesn't really work.. while i've often heard native speakers say "ich gehe zum Training" ... or "ich gehe zum xyz-Training" ... or even "ich mache heute abend Training" (I'm training tonight)...

don't think i've ever heard a native speaker use "trainieren" in the sense of "I do kendo/karate/taekwondo/whatever".... Likewise, I don't think "tun" would work either.. it would probably be understood, but I don't think it would make much sense.. ("Ich tue kendo")

"machen" doesn't translate only as "to make" ... it certainly can translate as "to do"

How do you do that? (Wie machst du das?) ... You do it like this.. (Man macht das so..)
Hurry up! (Mach schnell!) ... literally, "make fast"...

"machen" can translate several different ways into English.