So you've bought Freya and are just starting a game with her. Now what? Well, I'll walk you through an average game with Freya.
Build: Boots of the Magi I/II ---> Mana Pots/Meditate + Health Pots --> Polynomicon III
Build Explanation: I almost always start with Boots I, then buy Meditate and 5 health pots, so I can stay in lane and farm as much as possible. The reason I buy meditate is because I am very mana hungry, and meditate 2-3 times before I recall, and I wouldn't have enough mana pots to sustain in a lane without backing and buying more. To make a short explanation short, Meditate is renewable, mana pots aren't. Polynomicon is 2nd item buy after Boots of the Magi II, to start dealing massive damage with Pulse and Irradiate when you get T3.
Scenarios: The first ability you level up is Pulse. This turns your basic into ranged attacks, and does splash damage on a bunch of creeps, allowing you to farm effectively on the melee or archer creeps. However, watch out for enemy gods near the creeps, because the splash damage may hit them and cause the creeps to target you.
Next ability is Banish, so you can get away in case of some trouble. Just cast it on the gods and run. Remember to lead a little with this ability, because there is a very slight warmup.
Level 3 point goes to Irradiate. This is to farm more effectively, allowing you to KO the melee minions, then use Pulse on the archers.
After this, a typical ability preference would be Pulse --> Irradiate --> Banish while levelling up your ulti whenever possible.
Early game is a great time to be Freya, especially once you get your ulti. You can lay down some seroius harass with Pulse, and then close and pop Irradiate to lay down massive damage with your basic. If they still aren't dead after all that and have retreated into tower to recall, you can pop your ulti and tower dive effectively, because you can't be harmed at all by the tower. So remember: Harass, Close, Finish.
Build: Fatalis III ---> Gem of Isolation III/Void Stone III
Build Explanation: Attack speed is very important on Freya, because 2 of 4 abilities just buff her basic. So Fatalis III is important to get right away to get more attacks in with the buffs, and more dps in general. After Fatalis III, the rest of the build is really fairly flexible. If you're taking a lot of damage from mages, you might want to get Void Stone III for the extra power and protection. However, I normally get GoI at this point, for a couple reasons. Mainly because Freya can utilise GoI amazingly because her buff abilities (1,2) add magical damage to her basic, slowing the target even more. This is especially useful on Pulse, because the slow from the ability stacks with the slow from GoI.
Scenarios: Mid game is much the same as Early Game. Just keep harassing and keep scoring kills whenever possible.
Freya is also great at ganking at this point. Run up behind an enemy, pop Irradiate and start auto attacking, then when they're running away, slow them and rack up damage with Pulse. As long as the ally in that lane is helping out with damage, they should die fairly quickly.
Something to point out however, is to be careful with using Irradiate and Pulse at the same time. When using Irradiate at the same time as pulse, it gets rid of the splash damage and slow all together, which isn't good if farming minions or chasing enemy gods. The only time it makes sense to use them both at the same time is when you have Gem of Isolation III, and are only up against one god. They are still slowed by GoI, and the extra damage from Irradiate can be fairly substantial mid game.
Build: Gem of Isolation III (if you don't have it) ---> Rod of Tahuti III OR Void Blade III OR Obsidian Shard III
Build Explanation: Obviously, if you don't have GoI yet, you'll want to buy it now. Like I said before, it works just too well on Freya to pass up on, and the magical power you get doesn't hurt either. After GoI you have a few choices. If you chose GoI mid game, I suggest the 3 items above as choices for you. Rod of Tahuti III for the crazy power surge, VoidBlade III to rip through enemys protections up close, or Obsidian Shard III, to rip through magical protections with extra magical power. I would normally go for Rod III and Obbie Shard III, but I've seen people utilize Void Blade fairly effectively with Freya.
Scenarios: Late game is when Freya can deal out massive damage. By now, Pulse will be just ripping through enemy health from a range, and Irradiate will be crippling them in the close.
At this point in the game, you should be able to take down a tower no problem with your Irradiate. Run around and clean up all the enemy structures, then join in on the team fights. Make sure to use your Banish at the proper time to close with the enemy team and multi-ulti them. Also, don't be afraid to use your ulti as a moving Aegis Amulet. By the time a team fight is over, you'll be alive and walking and keeping the enemy team off your structues, and you'll have your 4 back by the time everyone respawns and regroups.
So that's it for now, be sure to check back for more. I'm not done this guide yet (Build Explanations!) so be sure to check back for more.