I'm trying to get into electronics and read that mouser is a good place. I wanted to buy a couple of leds, just like this one. But searching for "led" or "simple led" yields pages and pages of results. How do I search for components in this kind of store? Do I need to be super specific to get right results or am i doing something wrong?
Suppliers like Mouser and Digikey are less designed for beginner hobbyists and more for industrial use. The massive number of sometimes intangibly different options is most definitely a feature rather than an oversight. You can still use them, but it really helps to have some requirements in mind before going in. They're less about finding 'a small LED' and more about finding 'a through-hole LED with an intensity of 100 millicandela..., etc.' For example, starting with the 'LED emitter' category in Mouser and filtering based on which were in stock, through-hole LEDs reduced the results from ~36,000 to a far more manageable 2,600. If you had color or brightness requirements, you could narrow the field further.
In general, use sites like Digikey and Mouser if you have some requirements in mind, but if you're just window-shopping or trying to get an idea of what options are out there (without seeing several thousand at once), sites like Sparkfun or Adafruit are probably a better choice.
In addition to Alex's fine answer, there are a number of things you can do to limit your hits, or at least make sense of the long list. First, limit your list using every parameter you care about. Often this is surface mount vs through hole. For LED's, it will also be size and color, and probably current requirements. Also, limit your search to in-stock items.
Once you've done all this -- here's the magic. Sort your list by how many pieces the distributor has in stock and pay close attention to the first half page of hits that this method yields. Many will be duplicates of the same part packed different ways, or available in different packages.
This is not a perfect method by any means, but when a distributor stocks a ton of pieces of an item, it is often because engineers like to use that part. It could also be that the vendor likes dealing with some manufacturers more than others.
After that, you might consider cost (unless you are building a handful of something, and don't care), manufacturer (I tend to use manufacturers with generous sample policies, or at least those that don't give me trouble because of a '.edu' address).
After you have done some filtering this way, you should pore through the data sheets to make sure the part works for you.
Lastly, when you actually getting around to putting the part in the cart, put more than you think you need if you're doing the order for prototyping. If you need one piece of an IC, get a second for when you burn up the original, and a third for when you smoke the replacement. You'll save time (in the short run) and money (in the long run) if you do things this way. You might even consider buying a few of each candidate for some of your Bill of Materials.