You remember the old sales pitch for Othello: "A moment to learn, a lifetime to master"?
Every player will, at the beginning of each story, be granted five Drama Points for each of their attributes (for 20 total Drama points). More Drama Points can (and should) be gained during the story itself by the mechanism of Restrictions.
For any action you may spend either 1, 2 or 4 Drama Points from any single attribute. In the case of sub-attributes, the points can come from either of the primary attributes. These DPs will directly better your rank in the relevant attribute for that action. So if you are second-ranked in Warfare, in a swordfight with the first-rank-holder, spending DPs can help secure a victory.
One of the main benefits of having DPs is that they separate the things that you can do casually (walk to the corner store) from the things that you can do when it's needful (walk a tightrope) from the things that should be done only in desperation (walk the Pattern). Breath-taking actions should be rare... or rather, common actions are guaranteed not to be breath-taking. So by keeping the big things rare (by making you pay a limited resource for them) the system should encourage dramatic tension.
The second main benefit of DPs is that they shift some of the subjective decisions (on which the Amber DRPG rules are based) away from the GM and toward the players. I've never been particularly interested in telling people what they can and can't do. If I tell them they can walk down the telephone line in the rain then they want to do it all the time, and next time they want to do it juggling chainsaws. If I tell them they can't then they get all upset and argue about their decades training with the Ankh-Morpork thieve's guild. It's not worth the aggravation, it really isn't. But with the DP system in place I can just say "It'll cost you 2 DPs to walk down the telephone line... or I'll give you a DP outright if you make it halfway down and then slip". Let the player decide whether they succeed or fail, say I.