There is a nice answer for you to read on this link . Please visit it. It has nice pictures of how the process works.

The simplest experiment for finding carcinogens is called the "Ames Test" -unfortunately, you still need access to a special type of Salmonella bacteria and growth medium for the bacteria to grow on, which are hard to come by unless you work in a lab! Luckily, the procedure is short and relatively simple. If you're really interested in looking for carcinogens for your science project, I would suggest getting in touch with a researcher at a nearby university and see if they would be willing to help you out.

Here's how the test works:
You start with a strain of Salmonella that can only grow in the presence of a certain molecule called histidine. Histidine is an amino acid, meaning that it’s a building block for proteins! You and I need histidines to live, and so do most other organisms. Many strains of bacteria can produce histidine themselves -these are called prototrophs - and they can live happily on petri dishes even in the absence of histidine:

Read the rest and see the pictures on the "link" above.

There is no simple way to measure how much eating meat will increase your cancer risk. In general, it is extraordinarily difficult to determine which substances are carcinogens. Even the best methods are sometimes questionable.

Substances are determined to be carcinogens in a few ways. One is by looking at whether people that come in contact with the substance get cancer more often. This can be hard to determine because there are many factors that can increase cancer risk and it’s often hard to figure out if one of them is important. Also a substance can be tested for its ability to mutate DNA, which is how cancer usually starts. However, just because a substance mutates DNA in one circumstance doesn’t mean it that it causes cancer in practice. A third method is to feed the substance to mice and see if they get cancer. The somewhat obvious issue with this approach is that we aren’t mice so a substance may affect a mouse different than a human.

In the case of meat, experts decided that eating red meat and processed meat increase the risk of colorectal cancer by looking at a LOT of studies that used a bunch of different methods.

The one way to approach a science fair project of this type is to pick a specific known carcinogen in meat and measure its concentration. The issue with this is that the study found that eating meat increases cancer risk, without pointing out specific substances. So the conclusion wasn’t that a specific substance causes cancer, just eating meat in general. While this is an interesting scientific question, even the best scientists struggle with it.