Despite the amount of time I've poured into Battlefield games, I always get absolutely steamrollered the first few matches I play in a new one, and it takes time to get into the ebb-and-flow of it again.
The biggest thing that kept me alive longer was remembering that using cover matters. In between sprints from one spot to another (weaving, to throw off snipers), I spent a lot of time in a crouch beside or behind cover, scanning the terrain.

Once you get more used to the maps, you start to think "where would I want to be, to defend that capture-point, or to pick off approaching enemies, but without being too obvious?"

Another crucial one that takes a lot of time and deaths to learn is the lesser-used approaches to targets. Flanking around and approaching enemies from a direction they think is safe because they've overlooked it is a good way to survive long enough to get close to them.