Frost is a bit of a weird frame, where his original focus was more around being Defensive/Protecting Objectives has become less effective/relevant in more recent updates and has started to become fairly strong offensively.

Freeze is Frost's first ability and it's fairly flexible in how it can be used.

1. The first way to use it is directly hitting an enemy with it. If the enemy does not have Overguard/CC immunity, then it will be frozen in place.
2. The second way to use Freeze (currently bugged) is to aim it at the ground creating a marked zone which slows enemies walking through it. This is useful either in a choke point or around an objective where melee based units clump up.
3. The third way to use this ability is to pop Frost's Snow Globe, this is mostly just useful in case you placed your Snow Globe in a way that it obstructs your weapons or is no longer needed, I don't find the damage done by popping Snow Globe to be very useful.
4. Priming enemies with Cold Procs (+6 cold procs on regular enemies and caps at 4 cold procs on anything with Overguard) and Adding Cold damage to your weapons if you're using the "Freeze Force" Augment (combines with elements on weapons so not always desirable).

Ice Wave is Frost's second Ability and the Icy Wave Impedance Augment.

1. This ability casts in a narrow cone traveling along the ground. On its own this ability just adds +6 cold procs onto regular enemies hit, and is capped at 4 procs for enemies with Overguard/status resistance.
2. With the Icy Wave Impedance Augment, this ability becomes much more effective at slowing down enemies in a large area. The slow effect is the same as what Freeze would do if it were not currently bugged. Unlike the Freeze ability, Snow Globe, and Avalanche, this ability is not able to Freeze enemies (different status than cold) which is the actual Status that is required for Biting Frost to function.

Snow Globe

1. Snow Globe is Frost's main ability for protecting objectives. While I like this ability for lower level content, I find with recent updates that this ability has really become less useful for protecting anything on top of how fast late game enemies tend to destroy it. If I'm modding for this ability, I usually sticking close to base range and sometimes even using Narrow Minded to make it even smaller so that there's less of a chance for enemies to wander inside the Barrier, and also makes it much harder for a Nullifier to destroy your Snow Globe when walking into it. This also cuts down on how obstructive it can be to your weapons as you are not able to fire from the outside into your Snow Globe. Play around with range though, you may be more comfortable with a larger bubble than I am, and your other abilities do become less effective with reduced range.
2. Snow Globe will also push any non CC immune enemies away and briefly freeze them. You can also try the Chilling Globe Augment for a chance to freeze anything entering a snow globe, but I don't really feel this is effective, outside of leaving a bubble to passively defend an excavator when recasting Snow Globe will force freeze anything in range already, and also overlaps with Avalanche.
   Unfortunately Eximus enemies and enemies with Overguard have really diminished the effectiveness of this ability, and defensive focused frames overall.

Avalanche and Icy Avalanche Augment

1. Avalanche has become a very strong ability with the recent updates to Armor Striping, Biting Frost Augment, and more recently, granting Overguard when using the Icy Avalanche Augment.
2. Avalanche hits a wide area around your warframe and strips armor additively, meaning you can more easily fully strip an enemy in fewer casts with less Power Strength. This is pretty minor for lower level content but makes a large difference in the amount of damage enemies take later on. Enemies hit are also Frozen which will give you an increase to Crit Chance and Crit Damage if you're using the Biting Frost Augment.
3. If you run the Icy Avalanche Augment on Frost, you will be granted Overguard for every enemy hit by Avalanche. Overguard grants CC immunity to anyone that currently has it active (and for some reason immunity to Radiation even though that's Friendly-Fire and not CC) and provides a brief "Shield Gate". This is a fairly useful Augment for Defense Sorties with a Radiation modifier.
   Like Frost's other abilities (besides Ice Wave), this adds +6 Cold procs to nearby enemies and up to 4 cold Procs on anything resistant to status.

Biting Frost This Augment provides +200% Crit Chance and Crit Damage to any enemies Frozen (additive to Point Strike/Vital Sense style mods). It's unaffected by power strength. I consider this Augment to be fairly strong, especially because you will be hitting Frozen enemies which are essentially free headshots for even more damage. The only real downsides are energy management, and ineffectiveness against enemies that cannot be Frozen. It's probably best to run an efficiency focused build, and look to running something like Exodia Brave or Energy Generator. If you're far enough into the game for the Helminth, then Zenurik + Nourish also very strong for regenerating energy.

At the time of writing this, Frost Prime (and Mag Prime) are currently available from Prime Resurgence for another 120 days. You can exchange Aya with Varzia for some relics containing parts for either of these frames. Primes are not mandatory, they just have some minor stat buffs and look aesthetically different. If you don't care for a Prime Frame then there's nothing wrong with skipping it for something you're more interested in.