There are two ways of looking at the English Legal System - by Courts or by personnel.
The highest Court is now the Supreme Court. It is the final court of appeal in the English Legal systems. Although the European Court of Justice (ECJ) makes rulings which s2(1) of the European Communities Act 1972 requires the British courts to apply - "All such rights, powers, liabilities, obligations and restrictions from time to time created or arising by or under the Treaties, and all such remedies and procedures from time to time provided for by or under the Treaties, as in accordance with the Treaties are without further enactment to be given legal effect or used in the United Kingdom shall be recognised and available in law, and be enforced, allowed and followed accordingly" - there is no appeal to the ECJ. Preliminary rulings can be requested under Art 234 of the Treaty, but this procedure can only be used while an English case is in progress.. Similarly the European Court of Human Rights is not an appeal court. The Human Rights Act 1998 s2(1) says that "A court or tribunal determining a question which has arisen in connection with a Convention right must take into account any—.(a)judgment, decision, declaration or advisory opinion of the European Court of Human Rights...", and an individual can still bring a case against the British Government in the ECHR in Strasbourg.
The Courts can be classified into civil and criminal courts, although there are some overlapping jurisdictions. In general criminal cases will be heard in the Magistrates Courts and more serious cases in the Crown Court. Civil cases are generally heard in either the County or High Courts. The Court of Appeal is divided into a Criminal Division and a Civil Division. A diagram of the structure of the courts can be found here.
The Court's Service (HMCS) is responsible for managing the magistrates’ courts, the Crown Court, county courts, the High Court and Court of Appeal in England and Wales.
The hierarchy of the Courts is important for the application of the doctrine of precedent. The judgements of the Supreme Court (and its predecessor, the House of Lords) are binding on all courts below it. It can decide to break with its own precedents. The Court of Appeal is bound by the Supreme Court and its own precedents (save for the circumstances set out in Young v Bristol Aeroplane). Divisional courts of the High Court have adopted the rule laid down in Young's case although judges sitting at first instance are not bound to follow the decisions of other High Court judges although they tend to do so for the sake of certainty. Crown Courts can only create a binding precedent when a High Court judge is sitting. The decisions of County and Magistrates courts do not create binding precedent.
The correct way to an address a judge is set out here.
The Legal Profession is made up of Judges, Barristers and Solicitors. The judiciary includes professional judges as well as part time, lay magistrates. An excellent resource on the different types of judges and magistrates can be found here.
Individuals can be represented, or take advice from Solicitors or Barristers. The Law Society is the body which regulates Solicitors. It also oversees the training of solicitors - and designates which degrees are "qualifying law degrees". The Bar Council oversees Barristers.