As mentioned in part 1 of this article, the changes brought by the Evolution of Combat look more intimidating than they actually are. The main change is that the combat triangle is enforced, rather than simply being melee-dominant: Magic now almost always beats melee, for example, and you're now better off ranging magic-users than you are meleeing them in dragonhide.
Naturally, the other two combat styles are much better, boasting similar damage to equivalent melee weapons. Magic probably received the biggest change: combat spells in the normal spellbook only require elemental runes, and combat spells from the ancient book require fewer catalytic runes. This kind of balancing is most evident in free-to-play worlds. Non-members can now use blue dragonhide, bows up to magic (and rune arrows), and javelins. Mages have new sets, including books and wands, at levels 10, 20, and 50. Similar items were added in members’ worlds as drops from GWD enemies and from Dungeoneering.
Combat itself works in two ways now. Fans of the more relaxed old style can use the ability "momentum" in the Constitution section of the ability book to essentially toggle on the old system. For those who are interested in trying abilities, the in-game tutorial gives a very basic overview of how to use them, but it is very lacking on a more practical level.
You can use Dungeoneering on a low-complexity level as a way to play with abilities and with the action bar, and get a sense of how everything works. For most enemies you're just going to be firing off the basic abilities (and the occasional threshold ability) as soon as they're ready, but some might not suit certain monsters: It's generally not a good idea to use an attack that hits more than one target in an area with high-damaging enemies that are not aggressive, nor should you use abilities that lock you in place for its duration when you need to dodge an attack.
Why Dungeoneering? On low complexities, you get equipment that is mostly appropriate for your level for free at the start of each floor, and the rooms are filled with relatively low-threat enemies. Bosses use early versions of special attacks that would later be spread to both quest and "raid" bosses (such as they are), and so can be used to experiment with abilities and tactics without any risk.
Probably the most important step, however, is to have patience. While it has some similarity to the old combat system, enough has changed that you can't go into it expecting to pick up everything as easily as before. Start slow; ask some friends that have experience with the Evolution of Combat for advice; and as clichéd as it sounds, don't give up on it without giving it a chance.