First of all, when should you take the Frostbolt build?
You should use this build when you can safely poke from distance and you won't be flanked. I still think this is Jaina's standard, and therefore, safest build.

- Level 1 -
you can also take Lingering Chill, it helps reducing the problem of hitting the skill shot consistently, I prefer taking Fingers of Frost since it gives you a stupid amount of mana regeneration and when completed increases the damage of Frostbolt by 10%.
Using this build you should always be on distance when poking and only get closer to confirm a kill or to attack a picked target by the tank.

- Level 4 -
Having piercing on your Q makes your poke damage double if you can line up the shots correctly, so this is a very good talent to pick. Plus it also gives you faster camp clearing.
If you think you need the extra mana for very long fights you can also take Arcane Intellect, yet with this build you shouldn't be losing a lot of mana to get the work done, if you do run out of mana is because you are playing it wrong.

- Level 7 -
This talent should solve all your mana problems and increase your poking damage by a lot.

- Level 10 -
Normally, always take Water Elemental for slowing down their retreat while you poke at them until they die. Only take the ring for a specific wombo using this build.

- Level 13 -
Just take Icy Veins. Although Storm Front sounds very nice, Icy Veins just gives Jaina a lot of burst power.

- Level 16 -
Since you won't be close ranged for most of the fight I think taking Numbing Blast is the best choice, since you can Q, W and E to root and massive damage, then Q again to just obliterate your target. Northen Exposure can be taken as well, but I think the combo is just more destructive in this case.

- Level 20 -
Winter Mute shouldn't even be allowed in this game, in the right hands it can end the life of the entire enemy team, no matter their composition.

This build should be taken for massive amounts of damage when your team as a lot of CC. With it you need to be more risky than with the Forstbolt build, yet if you can follow up an excelent CC engage the enemy team has just completly lost the fight.

- Level 1 -
I like to take Fingers of Forst because I think it's important to have a lot of mana during the fight. You will be using Cone of Cold a lot. Lingering Chill is also a valid choice here, take it if they have a lot of mobility.

- Level 4 -
Once again, I think it's important to have extreme stock of mana. This also sinergizes well with the Build since you get more damage while above 75% mana, so you'll just blast them of their existence.

- Level 7 -
The soul of this build is the talent Ice Flows. It's CDR is insanely good, if you can chill 2 enemies, either buy hitting a Q, a Ring of Frost or a Blizzard, you can hit an E on both and simply have it again in 2 seconds. This is insane, you just blast them with an E, then wait 2 seconds, and blast them again.

- Level 10 -
For this build I think Ring of Frost can be a devastating choice for the enemy team. Since you'll pick this build when you have a good CC team composition if you can hit a good ring off that and then spam your E (And also all your other abilities) you can just blow the entire enemy team.
If they have some dive oriented heroes you can Water Elemental them and follow with your combos.

- Level 13 -
Of course you need to go Icy Veins for this build, if you can get your E for every 2 seconds after you hit a ring, imagine if you just have it almost instantaneously. It's an insane amount of damage.

- Level 16 -
Here I almost always take Numbing Blast since it helps you follow up with your next Cone of Cold. And just like always, you can get them under a Blizzard for even more damage.

- Level 20 -
Since you will be more close than usual I like to take Ice Blink for extra survivability in form of escape or for agressive plays, instantly chilling every one under a Blizzard, then rooting them with Cone of Cold, and if I have it available a Ring of Frost, turn on Icy Veins and you know what comes next, just sensure it if you are recording it.

I think this build should only be taken for sieging purpouses or if you can keep them inside the Blizzard range, for example, with an ETC Mosh Pit or a Leoric Entomb.

- Level 1 -
Since you will be using Blizzard for structures most of the time, you want to have as mush mana as possible. For this I also take Fingers of Frost.

- Level 4 -
For the same reason, if I am going to siege a lot, I prefer having the extreme mana stock, so I go Arcane Intellect

- Level 7 -
I always take Icefury Wand for CDR on Blizzard. This build is very situational, take it for sieging purpouses and if you can auto attack heroes as well, if they have threatning heroes that won't make you able to come close to auto attack, then do not take this build.

- Level 10 -
Just like the Cone of Cold build, hitting a ring will be the best way to keep them in place for your follow up combos. So here I prefer taking Ring of Frost.
If you want to split push a lot, you can take Water Elemental to tank towers, forts and keeps for you.

- Level 13 -
Take the extra casting range of W if you need extra safety or Icy Veins if you are safe to come a little closer. You can melt down a fort and shred a keep with the amount of spells you'll throw at them.

- Level 16 -
Get more damage on Blizzard by picking Snowstorm. This will help you get a lot more damage to buildings with the use of a single W.

- Level 20 -
If you took Ring of Frost, I tend to pick Deep Chill since the radius of Blizzard is now larger, making the enemies twice as slow will make them get hit by the second wave also, and you also apply even more effective CC for your team to out perform them. If you took Water Elemental I like to go Winter Mute because it will amplify the amount of damage you do to buildings and to enemies.