DtD uses the "Roll and Keep" system from 7th Sea and Legend of the Five Rings. Rolls are expressed as XkY, where you roll dice equal to X and keep the best Y of those and add them together. Most rolls are a skill and a characteristic, where you roll dice equal to your dots in the skill and characteristic, then keep dice equal to your characteristic. For example, you might roll Athletics and Dexterity. With Athletics 4 and Dexterity 3, you'd roll 7 dice (4+3) and keep 3 dice. It's a pretty simple system that lends itself to fairly stable results.
The Skills and Characteristics will look familiar to anyone who knows World of Darkness. The names are changed a bit for the setting, and some skills are different, but it's not terribly out of line. They get rated from 0-5 (6 in some really extraordinary circumstances).
You've got magic, swordsmanship, and skills. Magic is what you'd expect, casting spells. No spell slots or anything, just roll against the spell's TN to make it happen. If you're exerting your full power there's a chance of getting Perils of the Warp. Swordsmanship is, note, not just using a sword good. It's a system for building special attacks, learning new tricks and upgrades to build them with as you grow in power. Skils are the basic dots in your skills and the core of a character.
Each character is built with a Race, a Template, and one or more Classes. Races are your character race (Ork, Human, etc). Templates are supernatural additions (Vampire, Atlantean, Daemonhost, etc). Classes determine what you can purchase with XP. You can switch to a new class (or take the next level in an existing class) once you've bought all the manditory upgrades in your current class.
The setting is a mashup of Planescape and Spelljammer with 40k and a dabbling from everything else.