The Battle of Kaer Morhen - Kaer Morhen
The first part of this quest is all dialogue and story. During the dialogue you'll be given two options, the first of which is pictured above. You can choose to let Vesemir finish brewing Witcher Potions or let Eskel borrow the lab equipment to lay out the traps. It doesn't matter which of the two you choose, go with personal preference.
If you're curious which one is better it's Eskel's traps by far. Vesemir gives you the same sorts of potions you can make and only you will benefit from them.
Vesemir Potions: Superior Swallow & Superior Thunderbolt
Eskel Traps: Traps throughout Kaer Morhen's yard that only damage enemies
As for the next thing you're given a choice in, you'll have to choose whether or not to seal up the courtyard's wall or clean out the armory. Much like before, each option will change something about the battle. I'd recommend you choose the option to patch up the wall - the Silver Sword you get from the armory isn't that impressive and I didn't notice a difference in my allies from the armory option. Here is what will change depending on the option you've chosen:
Patch Up Wall: You'll fight less waves of enemies towards the end of the battle
Clear Armory: Every Witcher (including you) will have a new Silver Sword
When you finally regain control of Geralt all you have to do to begin the battle is leave the main room. There will be some scenes outside followed by the start of the battle. Throughout this battle you will switch back and forth between Geralt and Ciri. Aside from the fighting - what you have to do is very straight forward and requires no further explanation. Just follow the quest markers on your map/compass during each stage of the quest.
Tip: It may seem like you're timed but you really aren't. Be sure to take your time and loot all of the enemies - they drop some really nice stuff!
Once the battle ends you'll be treated to a long cutscene - when that's over you can continue with the next quest Blood on the Battlefield. Be warned - your answers to Ciri in the upcoming dialogue will alter the ending. Each time you get a timed event and have one or two options when talking to her you need to choose wisely. Read my guide for the right choices.