Awesome that you’re interested in ham radio!
What can I (legally) do with this thing without a license?
Listen, mostly. Baofeng radios are typically sold as “Part 97” radios (FCC lingo for “Ham use only and requiring a license”), although there are some models which are actually “Part 95” which would be GMRS/FRS radios. The GMRS/FRS radio model would require a separate license for GMRS, although that one is essentially an application + fee payment. It’s also not nearly as broad as a amateur (ham) license.
Edit: I forgot that the Baofeng radios can also transmit on frequency ranges that are technically outside of the legal ham/GMRS allowed frequencies, like business communications, police/fire, etc. Be warned that even with a ham license there will be some things you aren’t legally allowed to do with this device. It’s definately not a toy.
Any pointers for learning the basics on this particular machine?
Again, it will depend on the model, but personally I find the Baofeng/Chinese model radios a giant PITA to use. They’re cheap, sure, but aside from using the programming cable they can be much more difficult to program/use as compared to the Japanese models like Yaesu or Icom.
I should read the manual cover to cover, right?
Sure, I suppose. :)
Looks like it’s easier to program from a computer, any tips on that?
I can highly recommend CHRIP as good programming software. It’s also open-source: https://chirp.danplanet.com/
In the U.S., at least, the experience is roughly the same. I took my exam many years ago, but I was planning on giving a Tech license (the first license level) course this Summer and did a bit of research on how to get licenses these days.
The bulk of them are done online now through our VE orgs. License classes are fairly easily available, and I’ve heard of crash courses given during hamfests and field day.