Terror missions are somewhat unique in that you can get a general idea as to where the aliens are by where the civilians are dying - you can see the civilians even in the fog of war, and the aliens will be attracted towards them. During the alien turn you can also hear them screaming when they die - the camera tends to snap towards the civilians that are under attack.
Typically there are at least one group of chryssalids in a terror mission, which means that if you leave them alone for long enough, you're going to have big problems on your hands. Chryssalids also have no ranged attacks, which means that cover isn't a huge benefit against them.
My suggestion would be to try to move as fast as you can while still maintaining your defenses - if you don't have any idea where the aliens are, explore a couple of different directions early in your turn, while being ready to fall back if you encounter a particularly powerful alien group.
Remember that Assault troopers with Run and Gun can sprint and overwatch on the same turn, which can be powerful. Likewise, Support troops can get a boost to their ability to move without sprinting, which can make a difference. Snipers with squad sight should get to a vantage point early and try to inflict heavy damage as soon as possible.
Finally, don't neglect saving civilians, even if they're in an area with no aliens currently. Just moving within one square is enough to immediately remove them from the game. You don't need to cover their escape. This reduces the number of potential zombies/chryssalids and can keep your overall mission rating up without much effort.