While most people think that the YDS system is easy compared to the British rating system, I am not sure that is the case. In the YDS system, there is a rating, a grade, and a class.
The grade indicates the length of time the route typically requires ranging from I (the route takes a few hours) to VII (route takes a week or longer).
The rating refers to the quality of the protection and follows a pattern based on the Motion Picture Association of America. Within the YDS system a rating of G means solid protection and X means no protection. The rating is typically only applied to 5th class climbing (see below).
The class refers to technical difficulty and ranges from 1 (walking) to 6 (aid climbing). Fifth class, technical roped climbing, is the most commonly discussed and is subdivided from 5.0 (easy roped climbing) to 5.15 (really hard). Some of these subclasses are further subdivided into a, b, c, and d. Sixth class climbing is also subdivided. Historically, aid climbs were given a prefix of A and a numeric classifiers regarding difficulty with A0 being the easiest and A5 being the hardest. An A5 climb generally does not involve any "free climbing" (i.e., typical rock climbing where you are protected by a rope) and involves continuous stretches of aid climbing on body weight only placements (e.g., hooks, cam hooks, micro nuts, and bashies). An A1 climb involves continuous stretches of aid climbing but the placements can hold a fall (e.g., cams, nuts, and pitons). An A0 climb would involve continuous stretches of free climbing with the occasional aid climbing move. A classic A0 route is the Royal Arches route (5.6 PG A0 II). The majority of the route is moderately difficult free/rock climbing between adequate protection and takes 1/2 a day. It gets the A0 classification because there is a difficult (5.10b) traverse in the middle. This traverse can be bypassed by a pendulum off of fixed gear. Other A0 "routes" are free climbs that are too difficult for the climber and they pull on a piece of gear to bypass the crux.
In the early days of aid climbing, difficult stretches where protected by pitons, rivets, and bolts and a hammer (and drill) where key pieces of equipment. There has been a movement to do routes "clean" such that no trace is left behind (including scares to the rock). This lead to an additional prefix of C to denote aid climbs that could be done without a hammer (the ethics are a little more complicated). So for aid climbing you can have A0-A5 or C0-C5 depending on the difficulty and if you need a hammer/drill.
To give an example, most people rate The Nose as 5.8 C2 VI despite the fact that some people can climb it in a morning and others can free climb it (and Caldwell can do both). This rating means that it requires some moderate free climbing (5.8), can be climbed without a hammer but has some body weight only placements (C2) and takes multiple days (but less than a week) to complete.