Over the past decade or so, many yarn stores have moved from carrying piles of loose patterns to participating in Ravelry in-store pattern sales or simply carrying a handful of magazines and pattern books. Largely, this move resulted from the sheer prevalence of customers already having their pattern in mind before coming to the store and the lackluster sale of loose, printed patterns which simply resulted in dead inventory.
This change means that pattern searching has been reinvisioned with the ease of access to online materials. With hundreds of thousands of patterns available on Ravelry alone (and more than 516,000 available as direct Ravelry downloads), websites like AllFreeCrochet, AllFreeKnitting, Interweave+, Craftsy, and Knitty, plus the number of pattern books that are also available as ebooks, crafters have millions of patterns available at their fingertips. Again, this also means that typical LYS rarely carry loose patterns as their customers often do their pattern searching at home and come to the store with choosing the right yarn as their primary objective.
But, the availability of so many patterns at one's fingertips can be confusing if you are searching for something particular, especially if you aren't well-versed in the art of research or aren't quite sure how to navigate the internet.
Generally speaking, using one of the web browsers like Google, Internet Explorer, or FireFox probably won't be as helpful as you'd think. As I used to tell my students, when you type a word or a phrase into the search bar, these browsers do a basic keyword search, so the results will contain hundreds of thousands of links that happen to use some of the words that you typed, regardless of whether or not those words have much to do with what you are looking for. And, because web browsers have advertisers, the initial links that you see will always be ads for something--and most likely those ads won't have anything to do with the actual patterns you are trying to find.
Rather, the best way to find a pattern for a project is to use a more dedicated pattern collection page or site.
Most of the larger yarn companies and the bigger independent dyers have a page dedicated to patterns using their yarn, and this can often help you find a pattern for a particular yarn you may have purchased. For example, if you go to the Berroco website and are looking for a pattern that uses, say, Gingham, you can click on the link on the Gingham page that says "More Patterns Using this Yarn" and be taken to several patterns in Gingham--some that are free, others that are not.
Similarly, with, say, a Cascade Yarn, you can go to Cascade's website, click on Aegean Tweed or the yarn you are working with, and then click on the link under the yarn description which will take you to all free patterns designed specifically for Aegean Tweed.
If you would like search more broadly for patterns, the largest compilation for patterns--both free and not--is Ravelry. With Ravelry, you can search for patterns, designers, specific yarns, stores, etc. The way that I find Ravelry helpful when searching for a pattern is to use the advanced search where the limitors are on the left-hand side of the screen. So, if I wanted to search for a Man's Scarf and Hat set, after typing that into the search bar and selecting "patterns", I would then turn to the left side menu and begin limiting by selecting things such as the weight of the yarn that I want to use, the craft I'm doing (crochet, knitting, machine knitting, loom knitting), their availability (free, purchase online, purchase in print, Ravelry download, In my Library, Discontinued), the type of project I'm making, if I want a particular attribute (like colorwork or a particular technique), Size/Age/Fit/Gender, yarn weight, yardage, etc.
So, if I did type in Man's Scarf and Hat set, I'll get 45 different pattern matches. I probably won't use all of the limitors in the left-side menu because 45 aren't that many patterns, but I might choose knitting as my craft and DK weight yarn, which then narrows my results to five, which is more manageable to sift through.
Or, if I want to search for socks, I'll type in socks and get 72,101 results. So, I'll limit by selecting Free, Has Photo, Child, Fingering weight, and Single-Strand only, and will have 195 search results, which are much easier to scroll through than 72,101.
Sometimes, I'll search by using a theme by typing a word like "Ocean" in the search bar and then selecting limtors for knitting, sport weight, and 300 - 450 yards, which will limit the 1,856 patterns to 12.
If you are using Knitty, you can select Find Patterns + Features in their Knitty Library, which will prompt you to select what it is you want to knit or what you would like to read. From there, the pattern searching isn't as fully refined as Ravelry, but if I selected Gloves/Mitts, the patterns that crop up aren't too difficult to scroll through.
The key to keep in mind when searching for a pattern online is to be as specific as possible, but not so narrow that unless you were the designer/namer you wouldn't find what you are looking for. An example of something overly specific would be "Gray Man's Striped Cabled Hat and Scarf set." You would be better leaving the specific color out of your search because patterns can be adapted for a variety of colors.
Just remember to keep playing with your search terms, and doing so will lead you to some great patterns to try out.