a dialect is a variety of language used in a particular geographical region. It refers to the particular words chosen, (the word 'bread roll' has a number of different names in different parts of the country such as 'cob', 'bap' and 'bread cake') and also regionally specifically grammatical features (I weren't happy in Yorkshire, we wasn't happy in London)
Some linguists also include accent as a part of dialect.
Discourse is a word that causes much confusion - but it shouldn't! A discourse is any stretch of language used for the act of communicating (rather than an artificial stretch made up for, say, the act of studying, for example, to demonstrate how grammar works).
Discourse analysis means looking at aspects of a stretch of language, for example its style - and this includes its social, cultural, historical and contextual aspects as revealed by aspects of the user's stylistic choices.
A discourse might be a conversation, a discussion, a letter, a novel, a newspaper article, or whatever - discourses are everyday and everywhere and have been in existence since language began. We can usefully label individual discourses: 'the discourse of early 21st century broadsheet newspapers', for example; 'the discourse of 19th century working men and women'; 'medical discourse'; 'doctor-patient discourse', and so on.
Of course, we all have the ability to create discourses. When we speak, we know how to combine phonemes into words (or when we write, we combine morphemes into words); we then combine these words to make phrases, the phrases combine to make clauses, and the clauses make sentences on their own or combine to make longer sentences. Finally, we join sentences to make a text which is what forms our discourse - a discourse that we have instilled with certain stylistic elements that we have deemed suitable for whatever genre, context, purpose and audience we need to address.
When analysing a text, it can be fascinating (and gain many extra marks because of its subtlety) to dig deeper than the surface meaning of the words to try to reveal interesting cultural, societal or contextual aspects of the text's creator. To make this clearer, you can imagine that our own society is far more liberal-minded than, say, the society of a century ago. This aspect will show up in the texts written in these periods through a variety of aspects including word choice and grammar. Similarly, aspects of social hierarchy and social power always manifest themselves within texts. Imagine a conversation between a patient and a doctor, for example - again, discourse analysis seeks to reveal this.
An important part of discourse analysis is to determine what is called orders of discourse. In any discourse, it is clear that speakers or readers are rarely 'on equal terms'. Usually there is a hierarchy of power or a power relationship involved, wherein one participant - through language choices - can 'position' the other participant in a less powerful position. An analysis of men and women in conversation has revealed many ways in which apparently innocent uses of language create a power relationship between the participants.
Discourse structure is the study of how we combine sentences into longer passages to create a fluent discourse. To be effective, a discourse needs to be clear, coherent and meaningful. Discourse analysis sets out to uncover the linguistic and other means by which sentences are linked.
Form means the sound, shape and appearance of something, e.g. two forms of the word please, are pleases and pleased. The form of the sentence, e.g. 'He pleased himself.' can be explained by referring to two kinds of structure: that of its individual words (i.e. their morphology) and the way its words relate to each other (i.e. their syntax). The study of both of these aspects of sentences is called grammar. The study of the form of a text is called discourse analysis.
Formality is an important aspect of register. Informal language is friendly, familiar, and casual. Strict accuracy and correctness are not important in informal language. Formal language is authoritative, and more impersonal.
Speech tends to be informal, Writing tends to be formal.
Genre is a way of categorising texts according to similarities they share with those we already know. Texts that share content (e.g. chain saws, fondling couples), function (e.g. to frighten, to arouse), and form (e.g. books, films) are categorised and 'made safe'. But because, as they say, familiarity breeds contempt, genres can and do change – but slowly (see Pulp Fiction or Reservoir Dogs for evidence).
Genre is an important idea because it affects the production as well as the reception of texts. Writers know what we expect from a particular genre, and – to keep us receptive and comfortable (and hence – importantly for language study – more easily influenced or persuaded) – they will stay broadly within a particular genre’s expectations. Typical genres of fiction are adventure, detective and horror, and of non-fiction, reports (e.g. newspaper, school), biographical writing, advertising, recipes, etc. Taking account of genre allows you to comment on effective genre indicators and stylistic devices within a text. Texts may conform closely to the typical features of their genre, or challenge, mix and play with those genre expectations.