Here’s a really practical guide to using panel data: Longhi, Simonetta, and Alita Nandi. 2015. A Practical Guide to Using Panel Data. Seven Oaks: Sage. Based on course notes of a course taught for many years, this book deserves the word practical in the title. It contains the code and explanations to run your own panel analysis in no time. You’ll have to use Stata, and it only covers the British, German, and American panels.
I would probably recommend using this book in conjunction with one of the Green Books by Sage, e.g. Allison, Paul D. 2009. Fixed Effects Regression Models. Quantitative Applications in the Social Sciences (QASS) 160. SAGE Publications.
What’s great about Longhi & Nandi’s book is that it doesn’t pretend all data are textbook data: it starts with getting the downloaded data into shape and data cleaning. Even though the book is comprehensive, I would have liked it to go into more depth from time to time.