Scores and results
Zero is nil. A goalless draw is nil-nil. A clean sheet means a team conceded no goals, and it is credited to the goalkeeper and the defence as an achievement in its own right.
A brace is two goals by one player, a hat-trick is three. A fixture is a scheduled match. A tie can mean a knockout pairing across two matches rather than a drawn result, which is genuinely confusing and depends entirely on context.
Teams and people
A side is a team. The manager is what Americans would call the head coach, though in Europe the role has traditionally included far more control over which players the club signs. The gaffer is an affectionate term for the same person.
A club's supporters are not called fans by the club itself so much as supporters, and the distinction carries weight: the implication is a relationship you hold up rather than one you consume.
Shape and style
A formation like 4-3-3 counts defenders, midfielders and forwards, always from the back and never including the goalkeeper. Pressing means chasing opponents to win the ball back high up the pitch rather than retreating. Possession is simply the share of time a team has the ball.
The derby is a match between two clubs from the same city or region, and it is usually the most important date of the season regardless of where either club sits in the table.