There are a couple of ways to find a watermark on US stamps.
One way that costs nothing is to simply flip the stamp over and look at the back of the stamp. Sometimes the watermark is so strong, that it stands out to the unaided eye. This is especially true for the double-line watermark. I've had this happen a few times too with single line watermarks. Sometimes you can just flip the stamp over and "BAM!" – the watermark sticks out like a sore thumb.
The most common way to find a watermark is to use watermark fluid. You must be careful though because some inks are fugitive (i.e., they run or smear when they get wet). On all of the older US issues before 1940 where watermarks make a difference in the catalog number, I can't think of any US stamps where the ink is fugitive. But with foreign stamps, this is a different story.
The best recommendation I can give you is to use a commercial watermark fluid that is proven to work with stamps. Personally, I use the G&K brand of watermark fluid that I purchase from Subway Stamps. In older philatelic publications, you'll sometimes hear about other household chemicals used for watermarking. I would avoid using them. Many of them are flammable or poisonous. Some may even damage your stamps. A good commercial watermark fluid is the safest way to go.
If you're using watermark fluid, make sure you're using a black colored tray for the stamps. The neutral black background helps the watermark stand out more.
Flip the stamps upside down in the black tray. Depending on the size of the tray you're using, you can put more than one stamp in the tray at a time. Squirt a little watermark fluid on them. Give the fluid a few seconds to soak into the stamp. Then start looking for the watermark. Use a strong overhead light to look for the watermarks. You need to be quick though because the heat from the light makes the watermark fluid evaporate more quickly. I use my little desk lamp with a 100 watt bulb. When you're done, the fluid completely evaporates and you're left with a dry stamp again.
Watermark fluid works most of the time. But some watermarks are difficult to find, especially the single line watermark. Single line watermarks don't take up as much area. From my experience, they don't seem to be applied as heavily as the double line watermarks either. And lastly, if you look at the front of the Scott catalog, they show you diagrams of the layout of both the single and double line watermarks in relation to a full pane of stamps. Notice that the double line watermark is larger (width and height) and takes up much more area. Notice that the single line watermark takes up much less area. Depending on the placement of the watermark, sometimes only a small piece of the watermark may cross the stamp at a corner. Looking for single line watermarks is a tougher job.
If watermark fluid isn't helpful, there is one last step you can try on your own. There is a small device called a Signoscope. It's manufactured by SAFE (the same company that makes albums and supplies). You place the stamp on a small metal tray sandwiched between the tray and a thick piece of clear plastic. You insert the tray into the device. A lever applies pressure on the stamp – essentially flattening it out. There is a small 7 watt bulb in the device that shines over the tray. With the stamp flattened out due to the pressure applied, a watermark may be visible.
Signoscope devices are not cheap. They cost about $400 brand new. You might find a used one at a better price. If you're watermarking a lot of stamps or you're looking for very valuable stamps, then a Signoscope is probably a good investment. Because the Signoscope doesn't use any chemicals, this option is best too if you're worried about fugitive inks or other potential damage caused by watermark fluid.
I'll be honest and say that even the Signoscope isn't 100% perfect. Yes, it does a remarkable job. And compared to its cost, it's worth the price if you're a dealer or you’re a collector of more valuable stamps.
How do I watermark my stamps? I use watermark fluid most of the time. That does the job about 80% of the time. And it's cheap. It takes a little bit of time to load a stamp into the Signoscope device. That works for me for the ones where the watermark fluid wasn't conclusive.
The last method is to send your stamp in for a certificate. This works if you have a potentially valuable stamp and the watermark (or lack of watermark) isn't obvious. Expertizing agencies use highly advanced techniques for finding watermarks. These techniques cost thousands of dollars and they are cost prohibitive to most collectors. These agencies pay for those costs through the fees they charge to expertise stamps. Because their reputation is on the line with a certificate, they'll use techniques that are the most accurately available at the time.
If you haven't already discovered this, watermarks on yellow colored stamps are the most difficult to find. The ink is so light that when you apply watermark fluid, it soaks right through and the stamp design and everything is visible from the back side of the stamp. This is true for some orange-yellow stamps too. I have difficultly finding a watermark on yellow stamps with just watermark fluid. I almost always use my Signoscope on them.
Sometimes it's almost impossible to tell if a stamp has a watermark or not. The watermark is so faint, it's hard to see. Or the stamp is heavily cancelled and the black ink bleeds through to the back of the stamp. It's hard to find watermarks on these stamps too. There are some stamps out there that are going to be troublesome no matter what. In those cases, you're only choice is to send it for a certificate. It may be possible that the expertizing agency returns the stamp without an opinion if they are unable to determine the watermark too for some particular reason.
In those cases where the watermark can't be determined, you're only option is to assume it's the lesser valued stamp. Determine the possible set of Scott numbers it can be. Whichever one has the cheapest catalog value, that's what you should assume your stamp to be.