Puzzle and Dragons beginner's guide

I've now been playing Puzzle and Dragons for over a year, so I figured I might as well write up all the things I've learned!

P.S. Other PAD players - see anything I missed? Have any useful tips? Leave them in the comments!!

For those of you not sure what Puzzle and Dragons is, have a look at the official website. It's a puzzle based Pokemon-ish battle game in which you build teams of monsters and take on dungeons. It's available on iProducts, Android and Kindle Fire, and totally free to download. The game can have a very steep learning curve - as a beginner I made loads of mistakes and didn't understand many of the concepts, so I really hope this beginner's guide will help you guys avoid some of the same problems I had!

The best thing about Puzzle and Dragons is that the dungeons are constantly changing and the monsters are frequently updated with new evolutions, so there's always a goal to work towards. If you get burned out, it's easy to get excited the next week when there's a special event going on and a chance to get monsters you need and want!

There are two major ways Puzzle and Dragons is played - using in app purchases (IAP player), and not using in app purchases (non-IAP player). I am writing this primarily for non-IAP players, since I tend to lean that way when playing the game and I think it makes it more fun. :)