1. Find the company's support website!
Larger companies have support sections on their website. You can normally find them by going to the main website and finding "Support" or "Help & Support" on their main menu. Alternatively, you could try typing support instead of www when going to their website. For example, if you typed up support.nintendo.com, it'll take you to their support page. This won't work for every site though.
Once you're there, find out where their search feature is. It's usually right after you click "Support". It's best to specify the program you're using because if you just type up say "crash", then you'll probably have most of them irrelevant to your needs.
Some support sites may use suggestive searching, meaning as you type, it'll give you a drop down list of suggestions. This is a very handy tool.
2. Where to begin and refining your search
Looking on a search engine is like looking for a particular subject in the library. As a general tip, start specific, then broaden your search if you find the number of returns unsatisfactory, or the search results weren't good. But normally typing up what you're looking for exactly tends to yield pretty good results. Also don't write out in full sentences. Just nitpick keywords. Most search engines will filter out commonly used words so there's no point.
So say I have a problem where I'm playing a game and after five minutes of playing I get random artifacts on my screen (random pixels).
Using the general tip, I'd go "screen artifacts after playing game for five minutes" (most likely the word for would be omitted).
If I don't find what I want, I go broader: "screen artifacts when playing game"
And if I don't find what I want: "screen artifacts"
Although at the third point, I went too general and veered off what I wanted, so the second term should give me what I want.
If you get a pop up error or something similar, sometimes throwing what the error exactly says into a search engine will yield the results you want. Be sure to include the product as well. So if I get a "out of memory at line 85" error for a program called Awesome Painter, I go type up "out of memory at line 85 Awesome Painter". Unfortunately if it's not that common of an error, you probably won't get the results you want.
Basically, type up in a search engine a question you'd ask, but chop off everything but keywords.
3. Search engine operators
AND: Ensures that the terms you used are on the website. If you type up say Pokemon AND Pikachu, if the website does not have Pikachu or Pokemon, then it's not included. The & (ampersand) operator may work, but most sites use AND. However, this operator maybe obsolete altogether.
OR: Ensures that either term you used are on the website. So if you type up Pokemon OR Pikachu, then any site with Pokemon, Pikachu, or both will be picked up. The | (bar) operator may work as well, but most sites use OR.
NOT or - : Will not include the term you input. Do not put a space separating the word and symbol if you're using the minus sign. So if you type in Pokemon NOT Pikachu or Pokemon -Pikachu, then if the website has Pikachu in it, it will not be included. NOT maybe obsolete, so use the minus symbol instead.
" " : Surrounding your term with quotes means the engine will search for that term exactly as you typed it. If you typed up "Pokemon Pikachu", then only the results with Pokemon Pikachu somewhere on the site will be found. It's a good idea not to use this operator unless you're getting results that you don't want because the engine is messing up your terms. As an example, if you're looking for Devil May Cry 3 and you keep getting Devil May Cry 4, then you should use "Devil May Cry 3". Note that this operating will override any other operator inside of the quotes. So if you use "Pokemon -Pikachu", the NOT operator will not be used.
*: * is a wildcard, meaning any and all possibilities will be included. So for example, if you use Pok*mon, * can be any letter, number, or symbol. So if the website has Pokamon, Pokumon, Pok^mon, it will all be picked up.
site: : The site: operator, followed directly by a website address, a space, and some terms, will only look at that website for what you're looking for. If you use the root directory, it will search the entire website. If you use a page or another directory, it will only search there. For example, if I used site:www.serebii.net Pikachu, it will find all the pages were the word Pikachu is mentioned. But if I used say site:www.serebii.net/pokedex-dp/ Pikachu then it will only look up on the DP PokeDex where Pikachu is mentioned.