"So what exactly is counselling?"
This is a very big question!
Counselling is therapy aimed at allowing you (the client, or sometimes the patient) to learn about yourself in a safe and confidential environment. The environment is 'safe' in therapeutic terms as one in which no harm will come to the client - either physically or emotionally. It is confidential because the counsellor will ensure that the client remains anonymous, and that whatever is said within the walls of the counselling room will remain there as far as the therapist is concerned. In the process of learning about yourself and how you experience the world in which you live, it is possible to find answers to many of life's dilemmas.
So, if that is the basis of what counselling provides, how does it work with so many theoretical models and approaches to counselling?
It works through the essential aim of the counsellor to facilitate a relationship with the client, based on trust. Whatever chosen approach, or whatever models within those approaches are used, the essential force is the relationship. That is why, when a counsellor offers an initial session, perhaps called an assessment session, the aim is to provide a a period of time (usually up to an hour) for a sense to develop between counsellor and potential client that they can work together. This precious time can also be used to provide the answers to more practical questions such as cost of sessions, length of sessions, and gaps between sessions. There may be expectations and other questions to which both the potential client and the counsellor need answers, especially for the client if they have no previous experience of counselling. Often this first session will be offered at a reduced cost (typically half the normal fee) and not unusually it will be free. There will be no obligation to continue with therapy, at least not with most therapists and not at this point.
It is also often at this stage that a potential client, with no previous history of counselling or psychotherapy, will begin to become familiar with the differences in approach to counselling, as the counsellor outlines the way that they work. If there is no previous grasp of the differences in approach this could feel confusing, but there is much information on the internet which can help in the decision about which approach might seem relevant to your own particular worry - be it what is causing your concern, or in how you are dealing with it, or both.
As a brief guide to the basics of each approach, I will just outline what they are and very, very briefly, how they are different, and how they might be accessed.
If you visit your GP and ask for counselling - the therapy you are likely to be offered through the NHS is called cognitive behavioural therapy, or CBT. This is offered as a short-term therapy, often time limited. It is actually not counselling, but is a therapeutic approach in it's own right, and is the preferred option for the NHS because it has a record of efficacy which can be evidence based.
Psychodynamic counselling is offered by a therapist who might work in private practice, and who might also be called a psychotherapist. This term is often taken to mean that the practitioner has had a more in depth training, but there is some dispute about this so is best not to be too concerned about who calls themselves what - provided they are fully qualified and insured. It is also important that they belong to a recognised professional body, and best of all that they are on the Professional Standards Authority register. A therapist working psychodynamically will generally offer long-term, open ended sessions, and will focus on your unconscious self to provide answers to your current concerns. Psychoanalysis, more familiarly known perhaps as the Freudian approach to psychotherapy, opened the doors to later theoretical models such as Psychodynamic, Jungian and Adlerian. A psychodynamic therapist may refer to you as a 'patient' rather than a client, but this is not intended to mean that you are classified as having a psychiatric illness.
The humanistic approach encompasses the person-centred, or client-centred theory - and is offered by a therapist often in private practice, who works 'integratively' with other theoretical models such as transactional analysis or TA, and Gestalt therapy. All these models can also be offered exclusively by some therapists. The humanistic counsellor will also offer open ended sessions but this will sometimes mean that the work is short-term, which just means fewer sessions are needed. The basic belief which upholds this way of working is that it is the client who is the expert on his or herself, and that the therapist is there to facilitate the recognition of available resources already present in the client, but perhaps unrecognised. Therapy concludes when the client feels the time is right.
Solution focused therapy is another short-term and notably time limited therapy on offer, usually by an Employee Assistance Program or EAP, which might be available through your employer. This will be free to you, the employee, although the counsellor is paid through the contract between the employer and the provider of the program. This therapy is offered for between six and eight sessions typically, but can sometimes be accessed more than once.
There are charities and other agencies which can offer counselling with no charge, or for a minimal fee, in any or all of the above approaches, but there will often be a long waiting list before a counsellor becomes available. Some of these offer therapy for specific issues such as bereavement.
So that might have made some of the question more nutshell-sized, and I hope to have provided some guidance as to what everyone needs to explore before embarking on what might turn out to be the greatest voyage of discovery ever made.