I've noticed that they don't always explain stereochemistry very well. It's been 10 years since orgo for me, and I found the EK portion of stereochemistry lacking somewhat. So, I had to go to other sources to brush up (as well as EK).
Just remember that for two molecules to be Enantiomers, every single chiral carbon must be the opposite in terms of absolute configuration.
For Diastereomers, we have Cis and Trans, which is very straighforward. But then, remember that two molecules can be Diastereomers if they have multiple chiral carbons in the chain, and have at least one carbon that IS the opposite from the other molecule (otherwise, they'd just be different structural isomers). But, the difference is that at least one of the other chiral carbons on that molecule WILL NOT be the opposite from it's buddy molecule (the diastereomer). EK 1001 Orgo Questions has some good problems to help you with these. At least I found them benefitial.
I tend not to spot Meso compounds all the time. But, many times Meso compounds will present as 2 chiral centers. *The key here is that you can have chiral centers, while the molecule can be optically INactive overall. So, if you do an absolute configuration on each of the 2 (or more, but using 2 as an example) chiral carbons, they will be opposite in configuration (i.e. C1=R but C2=S). So, it's easy to see that the respective rotations would cancel each other out, to produce an INactive molecule.
I hope this helps a bit.