Level 1 - Frost Bite

Level 2 - Brilliance Aura/Crystal Nova

Level 3 - Brilliance Aura

Level 4 - Crystal Nova/Brilliance Aura

Level 5 - Brilliance Aura

Level 6 - Freezing Field

Level 7 - Brilliance Aura

Level 8-10 - Frost Bite

Level 11 - Freezing Field

Level 12-14 - Crystal Nova

Level 15 - Attribute Bonus

Level 16 - Freezing Field

Level 17-25 - Attribute Bonuses

Justification: Frost Bite on level 1 is a no brainer, great disable and nice to harass with. After that Aura is maxed, it's simply her best skill. You should get one level of Crystal Nova for the slow though, it stays the same on all levels, then Bite is maxed, then Nova for the damage. Freezing Field whenever possible for some nice AoE.

Variations: 

--Always get a chicken. Don't be a douche bag, just do it, chances are the rest of your team needs the money more than you do.

--If you have to buy wards right away because noone else is going to well then again just do it, it's all for the greater good. Since you won't have much money left I suggest getting a set of tangos and a couple of gg branches, if you need regen after that just use the chicken.

--If there's another hero that can buy the first set of wards (and there should be in most games) I suggest you get the items listed above. If you know that you'll be harassed a lot and/or like playing very aggressively you can get an extra healing salve or set of tangos instead of 2 branches. Sometimes starting with a magic stick might also be a good idea, for example if you're laning against a Zeus or Bristle Back.

--Another thing I sometimes do is buying tangos for another hero. When we use a Centaur+CM lane in a clan war for example Centaur usually starts off with a stout shield, a quelling blade and a flask and I pass him a set of tangos. That way we don’t have to pass the tangos back and forth all the time. It’s a pretty situational thing though.

--If you'd like to go for a different combination of items that's fine, just make sure your team has a chicken and a set of wards.

--In most games the first thing you should do once you get 200 gold is upgrading the chicken. Having a crow is simply much better since it's faster and items in a crow are actually safe; I'm pretty sure you'll never see a decent player use a chicken to buy his Sacred Relic from the secret shop. It's always useful, for your team as well as yourself, so you don't have to walk back to the base every time you want to buy a new set of wards.

--Around the 6 minute mark your first couple of wards will run out and you will definitely want to replace those. If you can afford it also start counter warding, especially when you know where your enemies have their wards.

--The first real item you should buy for yourself are boots. Most heroes get some other items like bracers first but since you're playing support that would delay your boots by too much, you need them for ganking and escaping ganks.

--Also grab a tp scroll and keep one for the rest of the game. Crystal Maiden is great for so called "save TPs". Basically anytime an enemy decides to tower dive to kill one of your allies you should tp there as fast as possible and freeze him in tower range. This will often save your ally as well as giving you a good chance to get a kill so always look out for those opportunities. (There are of course situations when you can not save your ally and you'll only suicide in the process, in that case you obviously shouldn't tp.)

--Next you should get a Magic Wand. You can get the parts earlier, both Magic Stick and gg branches are great for their price but getting Boots is usually more important than completing the Wand. This means that you might have to (temporarily) drop or sell a gg branch but really, it's not a huge loss.

--If needed you can also use the crow to get some regen (tangos or flasks) for both you and your lane mate. Sometimes it is smarter to simply go back to the fountain to heal though, I trust you can make that decision.

The last item I listed as "core" is Urn of Shadows and this item is simply amazing. It provides some survivability, comes in small parts but most importantly it has an incredible active ability that is invaluable when pushing but also great during and after ganks. Many people tend to skip this item when someone else has it already but due to the long cool down I actually think having two per team is ideal, three is still okay. If three of your team mates have it already though you should probably skip it and get a bracer or point booster instead.

The amount of heroes that Crystal Maiden can form strong lanes with is incredible and only matched by very few heroes. Here are some examples:

Note that many more are possible, being a ranged hero that doesn't need much farm and has a targeted disable means she can lane with almost any hero in the game, she works very well in tri lanes as well.

As Crystal Maiden your role is typically to initiate the ganks. If you can get in Bite range then you should Bite your enemy first and use Nova once Bite has worn off, otherwise use Nova to get into Range. Depending on the situation you can sometimes wait the entire 5 seconds before you Bite your enemy, often you will want to use Bite earlier though to prevent your enemy from running to his tower for example.

If you can get off a good freezing field then go for it. Many people think this spell is only good in team battles but let’s face it, in most team battles you get stunned and focused down anyways, Freezing Field is not like Black Hole or Overgrowth, the cool down isn’t as long and it’s just not as valuable. If it can get you a kill then go for it.

Team battles are definitely the most complicated part of DotA thus it’s hard for me to give you any specific advice here. If you can, then try to get in a good ultimate. This can be very easy at times, especially with a Tide or Enigma on your team or when you somehow managed to farm a Dagger + BKB. In other games it will be close to impossible. When your enemies have mass stuns while your allies have very little it becomes difficult. Just remember that if you stay alive and Bite and Nova repeatedly you’ll be far more of a help to your team than if you run in, cast a crappy Freezing Field for a second, then die. The gold you lose from dying is not so important, not being there to disable enemies however is. Thus you shouldn’t be too afraid of death; if you can land a good ultimate but you’ll die in the process then go for it. But charging in thinking “doesn’t matter if I die” isn’t a smart thing to do.

Also as with many other heroes always make sure you cast all your spells before you die, in team battles that usually means Nova first, run in, Bite, Freezing Field but really, it all depends on the situation.

As mentioned before Crystal Maiden should not farm much. She is one of the heroes that work fairly well with close to no farm, thus it is better to leave creeps to your allies most of the time. There will be situations though when there is little else to do. After a team battle in which all of your allies either died or lost so much HP that they have to go heal at the fountain for example you can not gank and there is no one else to take the farm so farming yourself is perfectly fine.

Warding is key in any decent level game. It helps your team in ganking, avoiding ganks, getting runes, picking the right battles and even in battles because you can have vision of opponents you wouldn't usually see.

As CM your job is to provide wards for the team. And the oh so popular "bought wards, they're on the chicken" doesn't cut it, you also need to place them.

I could probably also write a guide about warding but luckily others have done that already, so I'll just recommend you take a good look at this guide, it is very well done and covers most important ward spots.

The key here, besides knowing all the ward spots, is to be smart. Predict where the game is going and where wards are needed the most. Sometimes you might not need wards at all (usually when either team desperately tries to push the enemy base, though a ward in the enemy base can be very nice, especially if you have a Pudge or similar on your team).

Also note that during mid and late game you can use the crow for warding when you run out of item slots. Obviously the crow can not place wards anymore but it can still bring you wards, you pass another item on to the crow for a second, place the ward, give the remaining wards back to the crow and take your item again. This should not be done early game though because the crow is usually in high demand during the laning phase.