Plan, Prepare, Practice. Get under your truck (and inside the engine bay) and learn to identify all of the parts and know what they do. Do this at home and you'll get familiar enough with everything so when something is wrong, it's easy for you to identify. Sometimes what's broken is obvious to anyone, while other times it takes a keen eye to notice something is slightly off.
This goes in line with vehicle inspections. Not the state mandated ones, but what you perform pre- and post- trip, as well as daily while on the trail. Make a check list of things to go over and keep it in the glovebox. Make notes (if say the brake fluid looks low) and date them to track any changes. The fluid level will drop as the pads wear out, which is normal, but a sudden loss of fluid can mean a leak in the line. But you will probably notice a change in brake pedal feel first.
That takes us to knowing your vehicle. Some things will sound the same if your on the trail or pavement (like a leaky exhaust). But, you'll hear other sounds that only occur on the trail, or certain terrain. The only thing that can really calm your nerves is experience. Everytime you go out your confidence level should grow as you become more familiar with the vehicle, how it handles, and the noises it makes.
The same holds true once your back on pavement heading home. This is when I pay the most attention as getting to highway speeds for the first time after a trail can reveal an issue. You may not notice a slightly bent tie rod going 3-5 mph, but doing 75 mph you sure will! Mud may get thrown off the tires, or other parts, and hit the tire wells or under carriage. The sounds can be disconcerting if you're not expecting it. A chunk of snow can get caught on the inside of a wheel and cause a weird vibe, or steering shimmy if it's up front.
Talk to other owners of your vehicle and share their experiences. Get a workshop manual and study it. Know how your truck works and common points of failure. Carry spares with you and the tools to replace the part. Only you can instill the needed confidence in yourself to hit the trails. And never go out alone!