Alpine Grades are selected from many factors, including the technical difficulty, commitment, protection, and condition. Needless to say, each of these factors are influenced by many more subsections, as shown below;

Technical Difficulty; the technical grade of the crux pitch, or the climb as a whole. The technical difficulties always have by far the greatest influence on the grade a climb is given.

Commitment / Seriousness; the length of the route, the exposure you have to objective dangers (avalanche, rockfall, etc), the quality of the ice or rock, and the degree of remoteness of the route (especially with regards to potential retreat or rescue). On long or multi day climbs the possibility of benightment or getting caught in a storm or running out of food can also influence the grade.

Protection; this only really affects the grade when the climb is hard to protect, such as having lots of loose rock. Equally on some popular climbs all the belays are equiped, which makes it easy to retreat if necessary. If there is generally good protection, but say one spare section, this will usually be noted in the guidebook.

Conditions; the effects of altitude or prevailing bad conditions for a route generally give it a slightly easier grading than in perfect conditions at sea level.

It is normal practice for the first person who ascends a route, to declare a grade for it, and for second ascensionists to confirm (or adjust) the grade. All routes change over time, and whilst this is evident over a few hours on an ice climb, it is equally true for a rock climb where holds break and get polished. Therefore treat all grades with a big pinch of salt, as they are massively subjective, but do not ignore them altogether. I would be bancrupt if I had given a penny to everyone I had heard saying "the guidebook said it was a grade III, but in these conditons it was at least a V+", but it is not often you hear the quote the other way around, effectively downgrading a route. To me this is a classic example of an obsession with grades, that many climbers have. Grades are useful as advice, and for training, but to not become too focused on them or you will loose track of why you enjoy climbing. The best advice I ever got was "there are two grades; possible, and not-possible".

Alpine Grades
Given that grading routes is such a subjective task, do not be surprised to see the same route in different guidebooks with a different grade. Below is a table of the grading system that you will encounter when reading Alpine guidebooks. The letters (PD, AD, etc) can be applied to any type of climb, whether rock, ice or snow. I have given some examples of popular routes (mainly in the Mont Blanc massif) in each category, and an outline of the inclination of snow / ice, and the rock grades. Both of these are explained in more detail below the table.

WI Water Ice, hard ice formed from water.
MI Mountain Ice, softer porous ice formed from snow under high pressure.
M Mixed, both rock and ice are encountered on the route.

Like is the case with rock grading systems, there are also several different systems to grade ice climbs. Most systems are closely related to each other and take into consideration solely technical difficulty. US systems uses WI or MI to indicate the type of ice followed by the number to indicate technical difficulty. In Central Europe system is the same completed with Roman number (I-VI) indicating objective hazards (seracs, rock fall, etc.) to be encountered on the route. Finnish system is the same without consideration of the objective hazards. Scottish system (also used in Norway) uses Roman numbers to indicate technical difficulty of the route.

Grade Approximate Description (to give rough idea)
1 Low-angle water ice of 40 to 50 degrees or a long moderate snow climb requiring basic level of technical expertise.
2 Low-angle water ice with short bulges up to 60°.
3 Steeper water ice on 50 to 60 degrees. Possibly bulges of 70°-90°. Ice is thick and secure protection easy to place.
4 Short vertical columns, interspersed with rests. On 50 to 60 degree ice fairly sustained climbing. Ice is thick and of good quality. Secure protection is easy to place.
5 Generally multipitch ice climbing with sustained difficulties and/or strenuous vertical columns with little or no rest possible. Ice is still mostly of good quality.
6 Multipitch routes with heightened degree of seriousness. Long vertical sections and very sustained difficulties. Ice is often rotten with more or less dubious possibilities for protection. Mixed.
7 Full pitch of thin vertical or overhanging ice of dubious quality.
8 Hardest ice climbing ever done.

Aid Climbing Grades
Aid climbing grades indicates mainly the difficulty and quality of protection placements. Minor (upward) changes in difficulty can be marked with +-sign. Aid climbing grade are subject to change because of developing equipment and wear of the rock.

Grade Description
A0 Fixed pieces of protection are already in place. Possibly A0 climb can involve the climber placing slings to climb some passages.
A1 Pitons, hooks, wedges etc. are relatively easy to put in place. Occasional use of a ladder. Does not yet require much force and virtually every placement is perfectly capable of holding a fall. A1 climbs often get climbed "French free", meaning that the climber uses protection to aid progress by grabbing them.
A2 Protection placements are fairly good, but placing the pieces may not be without difficulties. Between good placements there may be some less perfect placements.
A3 A3 is hard aid. Normally leading a pitch takes several hours and there are potentially falls of 20-25 meters length, but without danger of grounding or severe injury. Active testing of soundness of placement is required.
A4 Serious aid. Fall potential up to 35 meters with bad landings. Placements hold only body weight.
A5 Placements hold only body weight for entire pitch with no solid protection. A leader fall at the top of an A5 pitch means a 100-meter fall with possibly lethal consequences.