I was in your same shoes a couple weeks ago and took it very slow and easy. Baby steps. Searched and read a lot.
1. Read the posts here and see what others have encountered. Issues will tend to fall into major groups - downloading the Application, starting to use it, and those who are using it but have questions about certain aspects. There are also posts about earlier versions and also an occasionally misplaced FCP 6 post.
2. Check out the various Apple documents available and there are a lot of them. There is some overlap between them but each one has something in it to offer. The last one is lengthy but good. It can also be good at puting you to sleep! Some of these are more useful than others and it depends on what answers you're looking for.
FCPX FAQs
http://support.apple.com/kb/HT5148 (good pre-purchase pre-purchase answers)
Version 10.1 Release Notes (lists the changes between versions)
http://support.apple.com/kb/HT4589
What's new in 10.1
https://help.apple.com/finalcutpro/mac/10.1/#ver3c4082710
How to back up important files before updating
http://support.apple.com/kb/HT5550?viewlocale=en_US&locale=en_US
FCPX Help: Update projects and events to 10.1
https://help.apple.com/finalcutpro/mac/10.1/#ver2df430747 (Also a good place to put in search words)
Updating and Working with Libraries FAQs
http://support.apple.com/kb/HT5958
Troubleshooting basics
http://support.apple.com/kb/TS3893 (11 step list for avoiding problems or trying to fix things on your own)
Managing Media with FCPX Libraries
http://www.apple.com/final-cut-pro/docs/Media_Management.pdf ("the" White Paper)
3. Back Up. That's what they all say, but video files are HUGE so it is a case of "easer said than done". If one doesn't have unlimited file space then the trick will be how to do this. Burning some items to a DVD is one way to save material but, again, video files are huge.
4. On-Line Tutorials: There are several available, if one can come up with the right search terms, that show how to get started. Some of those also are the beginning of a string of tutorials and the author would like you to subscribe, that's fine and I won't comment any more on that, but at least watch the first tutorial on how to get started.
5. Preping the Computer: It seems a lot of those that have problems may, and I use this word carefully because I don't know for sure, have limited computer capacity. Hey, the video files are HUGE! (have I said this before?) Most people have been dealing with little bitty files - documents, pdf, pictures, and watching stuff on-line. Once you leave the little stuff and get into video editing you're talking r-e-a-l-l-y B-I-G files. And, if that isn't enough, the new OSX system is designed to make optimum use of the computer to help speed processing. You need to free up ALL the resources you can.
a. Clean house of files, especially on computers that have been used for quite awhile. There is lots of garbage put on there in the way of everything from cookies to little pictures, etc. from all the web sites that have been visited. The computer keeps all kinds of information we don't even know about. Short of wiping the SSD or HD clean and starting over with a fresh install, at least one can clean what you can and create space.
b. Stop unnecessary processes: For myself, I prefer to disconnect my Internet cable. My Mac Pro does not have Wi-Fi and I don't use it for email or web surfing. It is only for video processing. My Mac Book Pro, on the other hand, is for all that other stuff and I use it only for, shall we say, emergency video processing, like when I'm away from home. When I get back home I clean it of the video stuff and it is happier.
c. Terminology: There is one term I kept coming across: "Volume". This has nothing to do with hearing. I've come across it before but didn't have to know what it means. Basically, it means something like a SSD, HD, or something that acts like one, like a partition, for example.
d. FCPX seems to like lots of space to work in so if the drive is fairly full then looking at a larger drive or another drive would be helpful. Some way to offload stuff and free up space is to err on the side of the angles.
Note: I'm just getting started on my first Library Project and encountered a problem importing an older X.9 video project (was "protected" from being "updated") and I'm trying to troubleshoot my workflow. So, basically, everybody's mileage may vary.
This is a great place to find answers to problems.
Hope this helps a bit and good luck. (I don't mean that facetiously 😉)