Chamonix is of course a world-famous resort, although really it's a group of separate resorts. Some of them go ridiculously high, but the cable cars up to the top are usually not included in the regular tickets. It's only a mere handful of miles from the Swiss border, and easily accessible from Geneva and Martigny.
For a zoomable, scrollable map of the area, see this online map using Openstreetmap or Opencyclemap.
Driving is the most popular way to do it. From Geneva there are fast roads almost all the way, including two tolls (EUR 1.50 and EUR 3) in both directions. Less than an hour to Les Houches, before you crawl through Chamonix itself, or out the other side past Argentière to Col des Balmes in about an hour and a half. Note that Chamonix isn't a single resort, it's lots of different resorts loosely tied together with a bus service along the valley. Transport between the areas is made a lot easier with a car.
There is also a train line running along the valley, making the scenic and precipitous trip from Martigny in around 1h10 (often with a short change at the border). If you're coming from Zürich you'll need to change at Lausanne to get to Martigny. From Geneva the train trip takes over 2h20 with 2 changes - it's much faster by car.
In March 2003 a day lift ticket for the Grands Montets area cost 33 Euros. In 2013, unless I'm misunderstanding the website, I can't find any day tickets for less than 43.50 Euros. Maybe there are other tickets available when you actually get there.
Not just a huge area, an immense area. Or rather, a large number of separate areas. The lifts are generally good, if a little old and slow in places, but in some areas such as Les Houches, there is a disappointingly large number of drag lifts.
Navigation is not that easy, with very little signposting. Even when there are signs, such as the big numbered signs on the side of the piste, these are essentially useless because they don't show the number of the piste, they just count down to the bottom of the run. The maps for Les Houches and Col des Balmes were also poor.
On the other hand, the snow can be fantastic, the combined area is enormous, and the views of Mont Blanc and the surrounding peaks (when they aren't obscured by thick cloud) quite awe-inspiring.
There is a large terrain park in Grands Montets, located near the bottom of the gondola lift. It is quite popular, even in the late March springy conditions, and has lots of banked curves, jumps, ridges, and a half pipe. Although it didn't look like it would survive for much longer into April.
Apparently a lot of the best and hairiest action in Chamonix is to be had off piste, with a good guide, in areas like the top of Grands Montets, or at the Aiguille de Midi, but we had to leave that for another day...
From the top of the big cable car 'A' in Les Houches, there's an unavoidable flat traverse to get over to the other lifts. And if you don't like drag lifts, beware of veering off to the right too soon (it's not signposted, but it only leads down to the drag lift).
There aren't any serious flat spots in Grands Montets, although with warm, wet conditions, the runs down to the gondola base, and from there across to the lifts to the right, can get slow.
The "official" site is at chamonix.com, which is now greatly improved from its previous poor state. There's additional information at ski-europe.com and boardnlodge.com. For Grands Montets and the Aiguille du Midi, see compagniedumontblanc.fr. Snow conditions are at snow-forecast.com.