Some dominants will use the concept of slave training as a way to subjugate their submissive or - especially - impress a potential submissive, by fostering the idea that they have knowledge that the submissive does not. Consequently, the submissive is led to believe that they need that dominant to provide them with some 'special' or even 'secret' knowledge and allow the dominant to 'train' them. Such training usually turns out to be nothing more than servitude, sometimes without even the fulfilment of the D/s dynamic.
It is rather like the "Pet Rock". It's just a rock, there is nothing special about it, its not like it really is a pet. But give it the label "Pet Rock," and dress it up a bit and it takes on a meaning of its own.
A submissive person needs no "training" to be submissive. The majority of dominants will take on a submissive whether they are "trained" or not, and many would prefer not to have to undo some other clumsy or inappropriate training before they can start teaching the submissive how they want things done.
In a long-term relationship, a dominant is likely to want his slave or sub to learn different skills, both to generally improve his/her usefulness to him/her and to meet changing needs. Most of these practical matters are not kinky and are things that any servant, housemaid, butler etc. would need to know.
While there can be some benefit to these things being learnt before being with a particular dominant, a lot of the learning will be for specific needs and for what pleases that dominant. The training may be done by the dominant or by other specialists, both external and within the BDSM lifestyle.
Examples of practical learning are how to make a cup of tea; how to give good oral sex; what type of sandwich is preferred in what weather; how to cook; how to shine boots; how to take care of toys in the toy bag; how to select the preferred wine; how to answer the phone properly; which of his hand gestures mean what.
A step on from practical education, but not as complete as mental conditioning, is having the submissive change their behaviour to suite the dominant. This takes time, and knowledge of both the dominant's desires and the submissive's current behaviour.
Behavioural changes can be anything from how she sneezes to the way she sits, stands, walks and kneels. It goes from the shallow things like how she prepares her hair to deeply-ingrained issues such as how she would deal with a rape attack.
A person entering into a total power exchange relationship as a slave will usually need to learn to submit their will to another person. It is easy to assume that this comes naturally or automatically to submissives but a submissive's desire to sublimate their will to another does not mean that they necessarily have the mentality required to cope with the consequences of that domination. (The same can be said the other way around - the desire to dominate does not automatically provide the knowledge and ability to do so.)
This is, in many ways, the much harder aspect of training and it is the part that most people know the least about and gets talked about the least. It is one reason why full, satisfactory Master/slave relationships are quite rare.
Some of this part of slave training can be undertaken by an independent trainer but it must be continued by the owner to keep the slave's mental positioning reinforced and growing so that the slave is fulfilled and happy.
The main process that is talked about in getting suitable mental transformation is internal enslavement. The learning curve for new masters is often very steep and involves a lot of things not usually found in BDSM web sites and books to make it all understandable and work.
Although there are a plethora of techniques widely available and easily found with any search engine, there are many factors to consider while training, the least of which is the terms of any contracts negotiated between a Master and slave and the most of which are a clear understanding of the goal of training, the likely best training approach and the need for reinforcement. Overall, the most effective training situation will exist when the Master has gained an understanding of the needs and desires of their slave and has also a keen acceptance of what s/he needs as a person. A careful mix of these two things, and not just a situation brought about by pure happenstance, will bring about a more fulfilling relationship for all parties involved.