I have super sensitive skin so I've been burnt before by trying on a new product and then having an allergic reaction or just my skin feeling weird. So here are a few tips and tricks to help when trying new products. And by products here, I really mean a skin care product but the same could happen with makeup.
First off, quality matters. If the product is of poor quality, the likelihood that something in it will make your skin react is higher. It doesn't mean that you shouldn't try it but just that you should proceed with caution. Also note that the generic products that you can find at the pharmacy will be comparable to the brand name but not exactly the same. Look for products that say "hypoallergenic" if you have uber sensitive skin. Even with these, you could react, but there might be less of a chance. Quality does not necessarily correlate with price but it often does.
Small area first
If you're unsure of the product (due to quality or other reason), try it on a small area first... and consider even trying out on, say, your forearm. If your forearm breaks into hives, it's not ideal, of course, but it's less bothersome most oftentimes than on your face. Now, the skin of your arms and of your face is not exactly the same so, while your forearm may not have reacted, there is still a possibility that the skin of your face would but the likelihood is much much lower.
Introduce one thing at a time
I'm a scientist so, when we do experiments, if at all possible, we try to change one parameter at a time. So, similarly, I recommend trying on one thing at a time. The reason is simple: if something happens, then you know that was the likely due to the new product. The problem when you're trying more than one product is two-folds, really: 1) should there be a reaction, you wouldn't know which one prompted it (and may need to go back a step and try one at a time) and 2) should you get benefit from the products (e.g., clearer skin), you won't know which one prompted the benefit. While the latter doesn't seem like a big deal, if you have budget constraints and want to purchase only one item, which one would you purchase?
Interactions between products
One thing that sometimes happens is an interaction between the products. So it's possible that the new product, by itself or in combination with other products doesn't make you react but, in combination with other products, may create an allergic reaction. If that happens, you obviously need to judge which ones you want to keep but, worst case, you just work them separately (e.g., on different days).
The caveat to the general rule of introducing one product at a time is that, if the products are from the same brand, you can try more than one product at a time. The products should be more or less similar formulations and most brands develop their products to work with each other, complement each other, etc. The interactions between products should be very minimal and you can generally rely on, if a product from a brand works for you, it's very likely that another product from the same brand would work as well. It's not 100% guaranteed, of course, as nothing ever is.
Pick your day
Pick your day when you sill sample a new product. If you have a big event, you'll be tempted to try a new fancy product because you heard good things about it but, let me tell you, that's a good way to invite a Murphy's Law. Should you react, you probably don't want to go to the event with hives on your face or looking like a scientific experiment gone wrong or something. And consider weekend vs. weekday. Depending on your job, your hobbies, events you have coming up, you'll have a preference for one vs. the other.
If you do react but you're not sure if it's a fluke or it really happened you can do a "challenge/dechallenge" test. "Challenge" is trying on the product again and seeing whether you react. "Dechallenge" is stopping the product and seeing if the reaction subside. Now, depending on the reaction, it may be hard to tell if stopping the use of the product is directly linked to whatever reaction you have. This is when the challenge comes in: if you want to be sure if it's the product, then use it again and see what happens. Note that you definitely DO NOT need to do this. But if, for some reason, you're wondering, you can use this method.
Developing a reaction to a long time product
It sucks but it sometimes happens that, for all that you've been using the same product(s) for a long time, you may develop an allergy to it. It happened to me with L'Oreal makeup (which is what made me discover MAC): I had been using those makeup products for years and then, one day, I reacted to them. My eyelids became all red and flaky. It wasn't fun. This is where the challenge/dechallenge can be most useful: if you want to be real sure that it's a developed allergy (and not something else that was going on that made you react), you can use that method to assess that.
Look at the list of ingredients
If you break out or have an allergic reaction, look at the list of ingredients. There might be something in it that you'll discover is your allergy trigger. I have a personal example of this albeit it's with tea vs. skin care/makeup products. I had bought a bunch of loose leaves teas... awesome stuff! I enjoyed those teas quite a bit. But then I noticed that, sometimes, I felt nauseous. It took me some time to connect the nauseous feeling with taking tea but I eventually did. The reason why it took me some time to make the connection is that not all teas made me feel bad. But, eventually, I realized that those teas that contained anise seed were the ones that made me feel nauseous. So the same could happen with beauty products or makeup: there might be one or more ingredients that make you react. So look into that and, if you notice a pattern, just stir clear of that ingredient.
Assessing the benefits
Obviously, if you're trying a new beauty or skin care product, you're hoping to get some benefit that you weren't getting before: clearer skin, smoother skin, less wrinkles, etc. With makeup, you will see the benefits right away because makeup is essentially colors on your skin so it's a straightforward thing. It's important to know, though, that, for skin care, you may not see the benefits the first day... it may take a week or several weeks to see the benefits. If you've ever received the "pouch" samples, that's generally not enough to know whether a skin care product will work for you or not. You will be able to know if you will have a bad reaction as those happen rather quickly generally. However, when it comes to the benefits, you'll have to take a chance and guesstimate whether it will give you the anticipated benefits or not. This is where the deluxe samples that you can get from Sephora, Birchbox, or other places are very useful: by having more product, you'll be able to assess better whether you will actually get benefits before investing for the full size product.