The word down can be used in a number of ways: as a preposition (followed by a noun), as in 'She was walking down the street', as an adverb, e.g. 'She lay down and fell asleep', after the verb 'to be', as in 'Shares were sharply down at the end of trading today', and as an adjective, as in 'He's been feeling a bit down recently.'
As a preposition, down can be used in informal British English without 'to' or 'at' when talking about a place that is near you, e.g. 'He's down the pub with his mates'. As an adverb, down can mean ‘going towards the south’, as in ‘Thousands of Scottish fans will be travelling down to London for the big match’. Down can also be used to mean ‘losing a game’, as in ‘At half-time, we were two goals down’, and (of a computer) ‘not working’, e.g. ‘I’m afraid our entire computer network is down at the moment.’
You can also use down to refer to the number of tasks in a series that have been completed, e.g. ‘That’s another exam over. Two down and four to go.’ If you are down for something, you have been chosen or are expected to do it, as in 'I'm down for babysitting on Friday evening.'
If something is down to somebody, they are responsible for dealing with it or making decisions about it, e.g. 'It's down to the prime minister to find out what went wrong.' If you are down on someone, you dislike them or disapprove of them, as in 'Why is the teacher always down on me? I've got low marks again.'