I feel I should preface this review by saying that I do not hate D&D 4E. My play group at the time gave the game a solid year of weekly game sessions before we decided to move on to the Pathfinder RPG. It is a fine system that runs smoothly; it just lacks some vital spark that makes it "Dungeons & Dragons" in my opinion.
Oh, and I'm also only looking at the first Player's Handbook, not subsequent ones.
Task ResolutionTask resolution in D&D 4E is accomplished by rolling a twenty-sided die, adding a modifier (or several) to the die's result, and then comparing the result to a target number. If the result is equal to or higher than the target number, the action is a success. This is pretty straightforward to explain to new people and there aren't any real variations.
Character CreationThe basic statistics are called ability scores and come with modifiers that are determined by how high (or low) the score is. In 4E, you don't roll dice to get your ability scores: it is point-based. In fact, this edition takes all the randomness out of character generation. Hit Points, which determines how much physical punishment anybody can take, are a fixed value per level. The whole thing looks eerily similar to how organized play works, since character generation is designed to be done without a Dungeon Master present.
So character creation then, boils down to coming up with a concept and making the numbers fit your concept. This concept could be as simple as "Dragonborn Paladin" (and picking your ability scores, race, class, and other stuff to fit) or as involved as making the most effective fighter (which means you're going to review everything and prioritize something to be the 'most effective' at).
There are three major areas where characters start to diverge immediately; skills, feats, and class features. Skills are how you do non-combat things like picking a lock or convincing the NPC that you really want that bow and he should give you a discount. Feats are kind of a catchall category for a variety of things that are not restricted to just one race or class but aren't a skill; armor proficiencies are an example. Class features are more properly called 'powers' in this edition of Dungeons and Dragons; they're the biggest part of a character's bag of tricks.
Powers, you see, can be used a specific number of times between rest. At-Will powers (such as Magic Missile) can be used every single round of combat. Encounter powers can only be used once between rests. Finally, Daily Powers can only be used once per day. Powers are defined by keywords, the attack type, the defense type, and the effects. Powers are the key to 4th Edition and your character will never seem to get enough through leveling. Fortunately you can pick up more powers through magic items, racial abilities, and sometimes through feats. Power selection is the main method that two characters of the same class are differentiated in what they can do.
Because a class values about three ability scores over the others, typically you will pick your class first, then assign your ability scores, and then pick race. Mostly so you don't accidentally hose yourself and end up with a terrible <YOUR CLASS HERE>. With a solid foundation, it is safe to pick skills and feats.
Once you have all that done (ability scores, race, class, powers, skills, and feats), it comes down to buying equipment with the 100 gold you have. And then you're done. It's not really all that simple to build a D&D 4E char when you start going into all the options you have. In fact, one of the issues I personally have with the character class section is that all the various class powers start looking alike
Doing ThingsFor the most part, anything outside of combat is done with skills. You are either trained or untrained in a skill and you have a total skill modifier based on a number of factors like character level. If the encounter warrants it, there's a kind of flowchart type deal a Dungeon Master will use called a Skill Challenge. This is the primary tool a DM will employ for non-combat encounters. It makes things a bit more challenging than a simple skill check.
Killing ThingsThis is why we play D&D, right? Killing things and taking their stuff. It is telling that the powers in the book are all geared towards tactical combat play; I can best describe it as a board game. Your oppositions and obstacles employ powers, skills, equipment, and ability scores in much the same way as you the player.
The lethality of D&D 4e is not very high. Players can heal themselves through healing surges, they have enough hit points to be tough to take down, and the rules for death are rather forgiving compared to what it could be. This is not to say that people don't die; it's just very hard for player characters to take enough damage to actually die.
The combat system is fairly detailed, as one might expect for a game that emphasizes tactical combat play. There's rules governing what kinds of actions there are and what actions fall into what category. Your basic attacks such as shooting a bow or swinging a sword are expressed as At-Will Powers in the combat chapter as well.
Fortunately a lot of the detail in D&D 4th Edition's combat is scaled. That is to say, you will not be using the whole thing right out of the gate. You will only need to learn more as you (or your players if you're the DM) grow in level.
ConclusionSo there's Dungeons and Dragons 4th Edition in brief. In my opinion it does not work as a role-playing game but as a scenario driven tactical board game. The problem with that is that there are other tactical board games that do the job with one boxed set instead of a dozen or so books, such as Descent. Ironically, somebody at Wizards of the Coast realized this and as a result there are a number of Dungeons and Dragons board games that are directly based on the 4th edition rules; Castle Ravenloft and The Wrath of Ashardalon, to name the first two.
But ultimately, you pay your money and you make your choice. I hope this review has been informative and helpful. I will also warn you that I will delete any comments that I deem to be inciting Edition War style arguments.
(2014/6/1 To my knowledge, there are no 4th Edition books still in print; the entire thing fell into limbo when Wizards of the Coast decided to start the big public playtest of D&D Next (what would become D&D 5e). There are PDFs available at DriveThruStuff though.)