If we are going to solve crosswords together then we are going to need a common language in which to talk about them. Let's start with the obvious:
A typical crossword is made up of an empty numbered grid of black and white squares and a set of numbered clues that contain all the information you need to enter a correct solution into the grid.
The number at the start of each clue corresponds to a numbered square in the grid. This number indicates where you should enter the first letter of the solution. The number in brackets at the end of each clue tells you how many letters the solution contains.
The clues are divided into a list of 'across' clues and a list of 'down' clues. These titles indicate which direction you should write when filling in your answer.
In a simple, quick or easy crossword the clue will be a definition and the task is to find a synonym or category item that fits the definition and enter it into the grid.
A synonym is a different word with the same meaning, eg: (priest/vicar, noise/racket, running/jogging). There are few if any true synonyms (i.e words that have identical meanings in every context) and, for the purposes of crossword solving, two words are synonymous if one can be swapped for the other in at least one context without a change in meaning. So the (noise/racket) pair contains synonyms because they have identical meaning in the sentences:
The noise was coming from the neighbour's house.
The racket was coming from the neighbour's house.
As one context is sufficient, it is irrelevant that 'racket' can mean other things in other contexts (a tennis racket, a gangster's racket, etc.)
A category item is a definition in which the solver is given a category and tasked with finding an example from within that category, eg: (pet/cat). Even in these simpler crosswords, solvers are not told which type of definition they have been given. So the answer to the clue,
1. Pet (6)
could be a synonym, STROKE (to pet a cat is to stroke a cat) or a category item, GERBIL (a gerbil is an animal that falls into the category 'pet')
Maybe this is obvious to you. If it is, good, it is nice to feel smart! But we'll need all the terms introduced in this opener when we start to deconstruct some cryptic clues.