Trailers use a very specific type of sound design, and few people even know what those sound effects are even called. Descriptors for trailer sound effects generally include:
Hits & Booms
Hits and Booms are exactly what their name implies. Sound effects that are big hits, booms, impacts, slams, whatever out there is happening suddenly whether it’s a traffic light turning on, someone slamming their fists together, someone landing hard on the ground. There’s a good chance these are getting emphasized with a hit.
Whooshes are for sweeping motions. They are often followed by a hit. Instead of thinking about cuts, think about fades, head turns, motion in general. They can be action-y, they can be flow-y, they can be ethereal or windy.
Rises also typically precede hits. Think of a helicopter slowly powering up, or the sound of a plane as it flies in from the distance then is suddenly very close to you. These build anticipation; when used well they keep you on the edge of your seat to find out what will happen next. You might not realize there’s a rise affecting your mood, but until you hear the end of it you’ll be somewhat unfulfilled.
Drones are for setting the scene or mood. Imagine a desolate apocalyptic scene; what does that sound like? A lot of times, a drone fills in that dead air. Not quite music, and also not just sound design.
NOTE: When you find a sound effects library, check their licensing information, because several trailer sound effects libraries license on a per use basis, and are not free to use willy nilly.
Here are the libraries I currently use for my trailers (royalty free). They range in price from free to a few hundred dollars each, but don't assume that the cheaper ones are low in quality!
Adobe Audition library - Adobe has an amazing FREE sound effects library that includes everything from ambience, cars, weapons, water, impacts etc. Did I mention it's FREE!?
Big Fish Audio Blockbuster Trailer - A great start to your trailer sound effects library, and very affordable!
Big Fish Audio Cinematic Sound Design - Another good starter library
Boom Library - Has a vast selection of sound effects libraries that include a handful specifically for trailer sound design.
Video Copilot MotionPulse - This library has a lot of action movie sound effects, and also some for trailers.
Hollywood Edge Sound Designer's Toolkit 1, 2, 3 - Sound Ideas is a pillar of royalty free sound effects in the industry. Since it's such an institution, a lot of their sounds might sound dated, but it's still a very versatile library.
GDC Audio 2017 Game Audio Bundle - 20+ GB of free sound effects! Royalty free, no attribution required!
I'm always on the lookout for more royalty free SFX libraries, so if you find any new ones, please send them along! I'm mostly on the hunt for libraries that sound less specific, by which I mean they're sounds that could be used in multiple genres instead of just sounding like they belong in a Transformers trailer.