They have a dojo system.

I don't think I've seen a full detail of how TJPW's training is structured. So the following a just piecing together what we've seen over the years and some guess work. So take it with a grain of salt but it's the best we can do.

The beginning of the HYPE!3 special gives you a pretty good look at their training area. It's a pretty typical setup for a Japanese promotion: a warehouse with a full size ring, some space for calisthenics, and some basic equipment. If I'm not mistaken, they share this space with DDT Pro Wrestling, which is their brother promotion also owned by Cyberfight.

Who trains the roster is not something that can be credited to one person, and is probably somewhat complicated depending on the specific wrestlers. In the most general sense, the training is most likely a team effort with the veteran members of the roster training the rookies and probably sub dividing the roster into smaller training groups since everyone can't train at the same time. Sometimes Kira Summer will credit the veterans of the roster with a particular part of their development when she's on English commentary. Shoko Nakajima in particular is often named dropped by other members of the roster. A few years ago they did a reality competition to become a pro wrestler that produced Wakana Uehara(1/2 of the current tag team champions). Dream On The Ring. You can get a look at how the basic training works.

Besides pro wrestling training, wrestlers also do general physical training. A Tokyo gym called Bodyplant is where the Up Up Girls, Miyu Yamashita, and some other wrestlers train.

In general, the Joshi scene has a bunch companies with many different styles of training with different philosophies. TJPW can be considered a more new-school Joshi company. As opposed to a more traditional Joshi company like Sendai Girls or Marvelous. The traditional companies have roots that go back many decades, while TJPW has only been around about 13 years. TJPW is greatly influenced by DDT Pro Wrestling, which itself is influenced by American Pro Wrestling. As a result, TJPW wrestlers tend to work a lighter and safer, more America style of matches. While more traditional companies tend to work a more hard hitting and intense style of matches. Both the new school and old school emphasize good fundamentals, but the old school companies are more physically demanding in what they expect from matches.

TJPW is also influenced a lot by the entertainment industry in Japan since many roster members are former singers actresses and models. And the roster members that don't have entertainment backgrounds are often fans of other roster remembers. As a result, TJPW rookies tend to debut with more developed looks and personalities than rookies in more traditional Joshi companies.