After you have the right tackle and have hooked that fish of a lifetime, comes the fun part - fighting the fish. It's a skill that takes experience to develop. Many people I guide or teach have never experienced fighting a large fish. They are used to just reeling in panfish like bluegills or bullheads. You have to get acquainted with your tackle and how it performs.
The best way to learn how to play big fish is to go out and do it! As a budding angler I spent a lot of hours carp fishing in the summer. Fighting carp is a lot of fun and you really learn how to wear a fish down, set your drag and/or backreel. So my recommendation is heading out to a proven carp water with a can of corn or some bread dough. It's great fun and a great way to sharpen your fish-fighting skills. Fighting steelhead or salmon on the Lake Ontario tribs is also a great way to get acquainted with hard fighting fish.
A couple other tips:
*Playing a fish is a lot like working a screwdriver without stripping the screw. You need to know just how much pressure to apply on the fish without the hook coming out or the line/rod breaking.
*Many anglers make the mistake of reeling the fish in too close to the rod tip - as if they could just reel the fish up to their hand. The shorter the amount of line you have out, the less stretch. The less stretch and give (via the rod) the easier it is for the line to get "shocked" and break. Rod tips snap easily this way. Also, if you take 4lb test and wrap it around your hands and try to break it with a slow pulling motion, you'll likely slice your hands. But shock it with a snapping motion, and you can break it. It's the same concept.
*When a fish starts acting crazy - like shaking its head or rolling in circles around the line, you need to ease up!