A triple beam balance is designed to measure the mass of an object. It is actually fairly easy to use once you understand how it works. A good place to start is by identifying the different parts of the balance. Starting on the left-hand side, you will see a round, flat disc that is parallel to the surface of the table. This surface is called the pan.
Extending out from the pan to the other side of the balance are three bars. These bars are known as beams. On each beam is a sliding weight. The beam furthest toward the back measures in increments of 10 grams, the beam in the middle measures in increments of 100 grams, and the beam in the front measures in single gram units. Both the 10 and 100 gram beams contain notches. The sliding weights must sit directly in one of these notches -- they cannot be positioned between them. 
On the far right side of the balance, there is a pointer that points at a line marked with a zero (0). Before adding any weight to the balance, it is important to make sure that this pointer is exactly at zero. If not, then your measurements will be off. If it is too high or too low, use the small knob on the far left side of the balance (under the pan) to adjust it until it is exactly at zero.  Once you do that the balance is ready to use. Here's how:
1. Start by placing the item that you want to weigh on the pan.
2. Move the 100 gram weight one increment to the right. If the beam drops below the zero mark, the item weighs less than 100 grams and you should use the 10-gram beam instead. If, however, it is above the zero mark, continue moving the weight to the right by one notch at a time until it falls below the zero mark. Once it does, move it back to the previous notch.
3. Repeat the above step with the 10 gram weight, moving it to the right one notch at a time until the beam falls below the zero mark. Once it does, move it back one notch and proceed to the 1 gram weight.
4. Slide the 1 gram weight to the right until the pointer is directly at the zero mark.
5. Add up all of the weights to determine the mass. For instance, if the 100 gram weight was at the first mark, the 10 gram weight was at the third mark and the 1 gram weight was at the fifth mark, the total mass would be 100 + 30 + 5 = 135 grams.
This can be a little hard to understand in writing. It is far easier to grasp how to use the triple beam balance if you can see it in action. This video does a great job of demonstrating how it works: