Any schematic capture and layout CAD package will have a learning curve, which can leave a new user searching for resources that will help get the job done. CadSoft's EAGLE schematic and layout editors are widely acclaimed as an easy way to get into PCB design, through no small effort on the part of the designers. However there are many resources beyond the widely ignored F1 help hotkey embedded in the program (yes, those still exist).
To start, many attribute EAGLE's success to their remarkable community. The active user base makes for high visibility to new questions, and CadSoft employees regularly respond to posts, infusing the forum with valuable expert knowledge. Searching there is the go-to when facing a problem, especially one that seems like it should have an obvious solution.
After creating a blank schematic page, a new user will want to start by immediately adding parts. There are a wealth of parts that can be added from the standard libraries that are included with the stock installation, but new users should be wary of simply adding unknown parts willy-nilly. It is tempting to add a schematic component that doesn't have the right footprint or pinout as a 'placeholder,' but putting that much faith in one's memory is probably a mistake. Instead, a new user can begin by searching out a part that has already been created. Element14 has a collection of part libraries that is particularly nice thanks to the searchable pdf that lists all manufacturer part numbers for the contents of the library. Always remember that any downloaded part is not to be trusted; spending 3 minutes verifying the pin connections and key footprint dimensions is well worth it!
If there are no decent parts that can be easily found in existing libraries, the designer can make the part themselves. Many people dislike creating their own parts because of the feeling that 100 other people have probably already done the work, but it is easy to fall into the trap of spending more time searching for a part than it takes to make it from scratch. In this case a manufacturer's datasheet, or perhaps an app note, will give all of the information required to create the required part. Once the 'suggested pad layout' documentation is found, Sparkfun has a simple step-by-step part creation tutorial that is so simple and complete that I saved a copy of it onto my hard drive. Although it may seem tedious, after creating 5 or 10 parts will quickly make searching for downloadable libraries seem ridiculous.
Once the board design is complete, a new user can save the step of producing Gerber files thanks to OSHpark's service which allows direct uploading of the EAGLE *.brd file. Their simple website and pricing scheme ($5 per sqin for 3 copies of the PCB) welcomes users to what is likely the easiest and cheapest way to get professional prototype boards made.
For those on a tighter time constraint and looking to save money by buying a PCB that only has copper on a bare board, BareBonesPCB by Advanced Circuits is another great place to go. They produce the boards in 24 hours, usually for ~$0.84 per sqin. However one should bear in mind that these simple PCBs lack solder mask, silkscreen, and many other attributes which will make assembling the boards more difficult. They also require the design be submitted with Gerber files, an extra step that that even casual PCB designers should learn at least by their second or third order.
As software packages are constantly changing, a user that plans to get serious about EAGLE will want to keep up with the direction of the tool. CadSoft does a great job updating their official facebook page by talking about new features, publishing resources, all without using it as a sales platform.
With these resources to start with, getting into EAGLE should be faster and easier, but there are many more that can help. If you have any favorites that you'd like to add, please suggest them in the comments!