No formal education is needed to learn finish carpentry work. Everything is explained in black and white all over the web, this site included.
A lot of it is absolutely free although some of the advanced trimming projects like crown molding or building hand railings may require a small payment for example an eBook. Usually the information that you pay for is almost always worth the money and you will end up with a wealth of knowledge with great value.
Everything is right here on the web that you would be taught in carpentry school and even more because often times the old tips, tricks and techniques used are not even mentioned in books.
Here is the kicker. Finish carpentry work is a trade that requires some practice and actually doing the work. You could read all the information in the world and that still won't make you a good finish carpenter. It will definitely help but nothing is better then taking this information and putting it into action on a project. Fortunately with this information and some practice it can be picked up fairly quickly.
Understanding the Finer Points
Once you have an understanding of hanging doors and casing doors and windows and installing baseboard the rest is easy short of the more advanced projects. By the rest I would mean running chair rail or shoe molding or even cap boards.
By doing these other types of trim work you will slowly discover that crown molding can't really be that tough. To be perfectly honest it's really not.
Here's where the money comes in. You will save yourself a bundle by doing your own trim work. Then when the word slowly gets out that you do trim work you will undoubtedly be asked to do some thing and then you will have to make up your mind if you want to charge for it or not depending on who it is.
My advice is to do a few of these small jobs for free as the power of the word of mouth is really strong when you do good work. I have even done a few bigger jobs for free and that has paid for its self time after time with more work.
Over time you will figure out that the effort you put in to learning finish carpentry was well worth it. The knowledge is invaluable and you will be able to apply these skills to many other trades besides just finish carpentry.
If you end up enjoying it as much as I did it won't take long before you're in business and doing some of the more advanced trim work.