On an analog clock, the hour hand points to the hour, and the minute hand points to 12 at the hour. At half past, the minute hand points to 6. Time is read as, for example, 'three thirty' and written as 3:30.
You already know that when the long (minute) hand points to 12, you read the short (hour) hand directly: if it points to 5, it is 5 o'clock. Now you are adding a second position to recognize: when the minute hand points straight down to the 6, exactly 30 minutes have passed since the hour began. We call this half past because 30 minutes is exactly half of the 60 minutes in an hour.
Think of the clock face as a circle divided in two. The top half (from 12 down to 6 going clockwise) takes 30 minutes for the minute hand to travel. The bottom half (from 6 back up to 12) takes another 30 minutes. When the minute hand is at 6, you are exactly halfway through the hour. Look at the hour hand: it has moved halfway between two numbers. If it is halfway between 3 and 4, the time is 3:30 — three thirty, or half past three. If it is halfway between 8 and 9, the time is 8:30.
Writing the time uses a colon: the number before the colon is the hour, and the two digits after the colon are the minutes. On the hour, you write :00 (as in 5:00); at the half hour, you write :30 (as in 5:30). When you read a clock, use a two-step check: first look at the minute hand to figure out whether you are at the hour (:00) or the half hour (:30), then read the hour hand to get the hour number. With practice, both positions become instant to recognize, and you will be ready to move on to times at 5-minute intervals.