First up:
Methods:
1) Self Training (The most common)
By hitting the Self Train verb, you will start "Boxing" in this state you will gain what is known as "Training Points" and Experience.
2) Training Points.
By Spending the Training Points at Yamcha, you are increasing your bonus of that stat every time you increase in levels, this applies to all stats except for stamina, where Stamina is just a set base stat increase.
3) Meditation.
Great for low level Characters, You will randomly gain stat increases, it's a fixed amount of 500, but it will not give you any experience to level up, thus you will not gain training points either.
4) Gravity.
Standing under Gravity gives you a huge boost to your experience, more so than self training, what this means is you level-up faster, but you do not gain as many training points in-between the level-ups, thus a lower level character may become more powerful than you are.
5) Killing NPC's.
NPC's are a great way (Especially Sagas) to gain experience and allow you to level-up faster, resulting in speedier level-ups and zenni bonuses.
6) Dragon Balls.
You gain a fairly large amount of Dragon Ball Wishes, there are boosts for every single stat, including Stamina, Ki, Strength, Defence, Speed, Powerlevel and even level-ups. - but you don't gain any Training Points in the process.
7) Quests.
There are several Quests through the game which offer increases in one form or another, be it a technique or a boost to a stat/stats which can increase your characters strength.

Gym.
The Gym is another great way to train, basically you sit there and hit the punching machine, or shoot ki blasts at the dummy, lift weights etc.
They give boosts to a stat, and is great for low levels, you do not gain experience from doing it, thus you wont level-up but it is great for low level characters and if you need more stamina.