Battalions work like this:
For a battalion to be implemented, you have to put the minimum amount described in the batallion on the battlefield, pay points for the units and the batallion itself. Also, you can fill up the batallion with the units described in the batallions. If not mentioned in the batallion rules, you cannot take any units not on the batallion into the batallion, but you can put them in the army outside of the batallion. The rules of the batallion just don't apply to them.
For sylvaneth in specifics: There are normal batallions like Free Spirits or Forest Folk, and overarching batallions, named Wargroves. A wargrove consists of a minor batallion and some extra units. If you want to implement a wargrove:
1. Pay points for Wargrove
2. Pay points for minor batallion
3. Pay points and put up models for the minor batallion (Attention: Most wargroves expand the amount of units of the minor batallion and even modify the type of unit!)
4. Fill up the Wargrove batallion with the needed units and pay their points
5. Every Wargrove says, that you can also put any sylvaneth unit. So your whole army can belong to the wargrove and use the wargrove rules, and can be set up as one.
-Every batallion gives you command points and an additional artifact. So if you play Gnarlroot, you receive these bonusses for the Gnarlroot Wargrove and the Household seperately. You can include up to 3 artifacts that way.
-The rules of the minor batallion just apply to the units mentioned in the minor batallion
-The rules for the Wargrove apply to your whole army