A pipe wrench is in a lot of ways the opposite of the Crescent wrench: Big, sloppy, with teeth that are meant to bite into the metal of what you’re turning and it will leave a mark.
You need one.
For over a hundred years (until the last few decades, when more and more copper and even more recently plastic has appeared), the pipes inside your house were mostly all iron. The pipes were cut to length by the plumber, who then cut tapered threads on the ends with a big loud machine, and screwed them into fittings (elbows, tees, valves, and so on). You have to screw them really tight or water will leak from the joint. And iron is relatively soft compared to steel.
Enter the Pipe Wrench.
The pipe wrench has a relatively long handle, and the jaws are serrated steel teeth designed to bite into the iron of the pipe or fitting and turn it (or hold it steady while the other side turns; like with the crescent, it often works best with two wrenches). The movable jaw is loose and sloppy so that when you need to reposition the wrench it’s easy to do that, and the teeth are pointed so that they grip in one direction and slip in the other for the same reason. Unlike a crescent wrench where it’s not the best idea to use it backward, with a pipe wrench it’s pretty impossible. (But I have occasionally used one sideways; gripping an elbow around the end.)
This is not a tool for finesse. Get one around a foot long for your first one (my go-to pipe wrench around the house is a ten-inch, and the second is a fourteen). As with the crescent you’ll soon want or need a second one to turn the other half of what you’re working on, and by then you’ll be able to judge whether you need more force (larger wrench) or the ability to get into a smaller space (smaller wrench).
Adjust the jaws so that both sides are hitting the pipe and ideally the back of the movable jaw is not. Hook the wrench around the pipe and pull. The jaws should bite into the surface of the pipe and turn it. If the jaws are slipping and not leaving ugly marks, adjust the wrench a little tighter. If they are leaving ugly marks and the pipe is not turning, try a bigger wrench. If that doesn’t help, consider what else you might do; it’s entirely possible that the pipes are rusted tight together and not ever going to come apart. You may need to move further away from your problem to another joint and end up replacing more than you’d planned.
Do not use a pipe wrench on plastic pipes. You’ll just crack them. The situations where it’s the right thing to do to use a pipe wrench on copper are almost non-existent as well: think twice and then think again. If you’re trying to get a valve unscrewed from a fitting that was soldered onto the end of the copper pipe, hold the fitting steady with a crescent (or if you must, a pipe wrench) and turn the valve carefully. It’s easy to twist copper pipe and make the soldered joints fail.