Here is a list of trainers and training locations you can have so you can learn certain attacks and skills. Strength Training increases your Physical and Critical Hits. Speed Training increases your Evades. Defence Training increases your Blocks. Ki Training increases your Ki Attacks. Note, new attacks and trainers may be added from time to time.
King Kai
You must be dead to see King Kai or you can Instant Transmit to him. When you train under King Kai you can learn four things. You can learn Kaoken, Spirit Bomb, Telepathy and Telepathy Control. Each takes a 6 days to learn except Telepathy Control and Spirit Bomb takes 9 days to learn. You also train under 10x normal gravity on his planet so your Power Level should rise a bit while training with him.
Master Kai
You must have competed in a Tourniment in the Other World and won. Master Kai can teach you Fuse and the best attack of all time...Dragon Fist. Takes 6 days to learn Fuse and 10 days to learn Dragon Fist.
Guru
You must be on Planet Namek and he will train anyone. Guru will not train anyone who has some evil in them. Guru draws out your hidden power and trains you to learn a healing move. Healing works like a Senzu Bean and you can use it on anyone but yourself. Hidden Power doubles your PL. This is a great trainer if you wish on having a higher Power Level and if you have a team that needs someone with a healing move. Takes 8 days to learn everything Guru can teach. You can only train with Guru once.
Dende
Dende can only train you if you are on Namek. While training with Dende you can learn 3 things in a short time. You can learn healing, you can learn Speed Training and you can learn Mystic attack (Nameks only). Takes 8 days to learn everything, but only 5 days to learn Speed Training and healing. 7 days to learn Mystic attack.
Piccolo
On Earth only. Piccolo trains a 6 days at a time. Every 6 days you learn something new. Piccolo can teach you Special Beam Cannon, Mystic attack, Speed Training and Defence Training.
Goku
Goku can train with you on any planet because he has Instant Transmission. It takes 6 days to learn one attack at a time. He can teach you Instant Transmission, Rogafufuken, Kamehameha (if you already have it, you can train for a stronger form), Speed Training and Defence Training. Goku can also Upgrade Instant Transmission and it takes 9 days.
Trunks
On Earth only. Trunks can teach you how to handle your swords and weapons better. If you train with Trunks, the power of your swords or weapons will increase. You can also train for Burning Attack, Nova Blast, Finishing Buster, Trump Card, Defence and Power. Takes 6 days for each. Also when training with trunks you can train for weapon training which will increase the number of weapon attacks you can do, Takes 4 days for that.
Gohan
On Earth only. Gohan can teach you Masenko and Barrier. He can also upgrade both. Takes 6 days to learn each attack and a 6 days to upgrade.
Goten
On Earth only. Goten can teach you Kamikaze Ghost Attack, Makosen, Kame Kame Ha and Galactica Donut. He can also upgrade any of the attacks to become stronger. Takes 7 days for each and 7 days to upgrade each.
Vegeta
On Earth only. Vegeta is possibly the best trainer you can have, but because of his own pride and feelings, it will take longer to learn everything you want. Vegeta can train you to learn Final Flash, Gallet Gun, Big Bang, Ground Flare (stronger forms if you already have these attacks), Speed Training, Strength Training & Defence Training. It takes 8 days for Final Flash, and 6 days for everything else.
King Vegeta
On Vegeta only. King Vegeta is the King of all Saiyans. So he nows most of the Saiyans attacks. He can teach you Moon Blast, Oozaru, Controlled Oozaru, Kikoho, Koshoku and Galic-Ho. Takes 6 days for each.
Frieza
Any Planet. Only Evil and Neutral can train with Frieza. Frieza can teach you Death Disk (Frieza can upgrade it to 2 Disks if you already know Death Disk), Frieza Beam, Death Ball (Frieza's strongest attack) & Haretsu No Maho. Death Disk and Frieza Beam take 4 days each, Death Ball and Haretsu No Maho take 6 days each. Frieza is a good trainer for Evil fighters.
Cell
Trains anywhere cause he has Instant Transmission. Cell may seem like a great trainer because of all of his skills...and he is, but it takes a long time to learn each thing. He can teach anything the other trainers can teach except for Final Flash, Healing, Demon Form, Instant Transmission and Super Saiyan. He also can't upgrade any attacks to form stronger forms. It takes 6 days to learn something from Cell and you must Be evil ONLY! Cell is the only one who can upgrade your regeneration skills to perfect form, but it takes 1 week.
Tien
On Earth only. Tien Teaches Tri-beam (or a stronger form of it) solar flare (or a stronger form of it) and Multi-Form. Multi-form can come in handy when training in the Hyperbolic Time Chamber. Takes 6 days for each.
Kame and Mr. Popo
On Earth only. While Training on Kame's Lookout, you can learn Fusion and Mystic attack. Takes a 6 days for each.
Android 16 and 18
On Earth only. Dr. Gero's Androids can teach you Speed Training, Defence Training, Strength Training, and Ki Training. They can also train you for a perfect Kamakazi that will kill your opponent without fail. They train anyone of any race and it takes 6 days to learn each technique.
Android 17
Any Planet. Android 17 decided he would rather work alone. His sister doesn't realize this, but even though she cares for 17 very much, 17 could care less. Android 17 trains anyone as long as they are willing to put up with him. He teaches Electric Blast attack and the dreaded STOLEN ENERGY!! It takes 6 days to learn electric blast attack and it takes 8 days to learn stolen energy.
Ginyu Force
Any Planet. These guys are the biggest bunch of weirdos you'll ever meet, but they are able to take time away from posing and looking pretty to train anyone of any race. They can teach you Fire Crusher Ball, Purple Spiral Flash Attack, Genocide Attack, Mouth Blast, Speed Training, and Stength Training. These attacks may not seem too powerful, but while training with the Ginyu Force, these can be some of the strongest attacks you have! Takes 6 days to learn each move and 5 days for Speed Training or Strength Training.
Rose
On Earth only. Rose teaches all the Dragoon attacks available. It takes 7 days for each attack. She can also upgrade all attacks.
Ryoko
On Earth only. Ryoko can teach you all of her attacks available on the attacks page. It takes 6 days to learn each attack, but nothing can be upgraded.
Pikkon
Anywhere in earth, King Kai�s, Earth, Or Other World. Pikkon can teach you Flaming Kick or Thunder Flash his strongest attack. Takes 6 days to learn Flaming Kick and 12 days to learn Thunder Flash.
Hyperbolic Time Chamber
On Earth only. You spend 7 days in here. While in the Time Chamber, you train for Speed, Strength and Defence.
Planet Training
You can just fly to a planet and train under its gravity. The higher the gravity, the more powerful you become. Stay there as long as you want.
Partner Training
If there is a member with a move you don't have and you want to learn, train with him/her for 2 to 8 days depending on the attack to learn it. The trainer can ask for any payment to train you for the move though.
Self-Training
You can train yourself for any attack on the attack page. Attacks will take double in which it takes a trainer to teach you.
Despiration Attack Training
Finally, you have the chance to train under any member and learn his/her Despiration Attack! This is a great way to surprise your opponent with an attack he wasn't expecting. You train for the attack for 1 week and the trainer can ask for any fee he wants. Trust me. Its worth it!