Grade One Music Theory Requirements
In Grade 1 music theory you need to know three time signatures:

The Bottom Number
The bottom number in a time signature tells you the type of beat we need to count in each bar. The number 4 represents a crotchet beat. So, in Grade One music theory we only need to think about counting crotchets.
The Top Number
The top number tells us how many beats we need to count in each complete bar.
So,
means we should count two crotchet beats in each complete bar
means we should count three crotchet beats, and
means we should count four crotchet beats.
Barlines
We draw vertical barlines through the stave to divide the music up into complete bars. (Sometimes the first and last bars of a piece can be incomplete, but all the bars in between must be complete ones).
Here's an example in 2/4:

The values of the notes in each bar always add up to two crotchet beats.
Here's an example in 3/4. This time the first bar is incomplete:

The values of the notes in each bar add up to three crotchets, except in the first and last bars which are incomplete.
Working out the Time Signature
In the Grade 1 music theory exam, you might have to work out the time signature of a short piece. How do we do that?
First, pencil the value (length) of each note underneath it, in the same way as you saw in the previous two examples. Then carefully add the values together. You should get the same total in each bar. If you didn't, then you've made a mistake so check your working out!
Don't forget that in the Grade One music theory exam, you only need to know 2/4, 3/4 and 4/4, so the right answer must be one of these three. You'll never be presented with a tune that changes time signature in the middle of the piece in the Grade One music theory exam (but you'll have to do that in later grades!)
Try this practice question. Hover your mouse over the music to see the working out and the correct answer:
Adding Missing Barlines
In your music theory exam, you might have to add the missing barlines to a short tune with a given time signature. How do we do that? Let's work out where to put the barlines in the following melody:

First, look at the time signature. How many beats do you need to count? (Don't forget, the top number on the time signature tells us how many to count.) In this melody, the time signature is 3/4, so we need to count three crotchets in every bar.
You'll always get the first barline drawn for you, as an example. It's a good idea to pencil the note values in as you do this exercise too - it's easier to work out where you've made a mistake and to double check your answers if you've done so. Let's pencil in those note values:

Start adding together the note values until you reach the number you need - remember it will always be 2, 3 or 4 crotchets in the Grade One music theory exam. Then draw a barline, (use a ruler for neatness*).
Then start counting again. Repeat the process until you get to the end of the melody.

Your last bar should also have the full number of beats (in the Grade One music theory exam that is, but not always in real life!) Double check your answer - go back and count each bar again. If one of your bars has a different number of beats to the others, you have made a mistake!
Make sure that your lines are totally vertical (not leaning to one side or the other), that they don't poke up higher or lower than the staff, and that they are placed about one note-head's width away from the note on the right. Look at the first barline that you were given as an example, and use it as a guideline.