Plumbing is a skill trade. Good plumbers make good livings at it. There are many "rules" and practices that take time to learn. Some of us hobbyists have picked up enough to make some repairs or run some lines. My father in law started teaching me 40 years years ago. You can learn it too. It takes time and practice for sure. I can't cook hardly at all. But I suppose I could learn it. It would take time.
I recommend you find a big box store and pick up some how to literature on plumbing basics and start reading. You can learn about hot and cold water lines, faucets and toilets, drain traps and drain lines, shut off valves, seals, etc. The connecting fittings take some time to learn, such as tees, elbows, connectors, and all their variations in size and type (steel, copper, PEX, ABS, etc, etc.) I still get embarrassed asking for pipe nipples. But that's what they're called.
Open the cabinet under your kitchen sink and take a look. Find the p-trap, drain connections, hot water line, cold water line. You can see some of the variety. And all of those "water conduits" were fabricated through walls, floors, etc.
Installing new plumbing in an old Airstream is a major project. It starts with a plan on where all the fixtures will be, and where all the drain water tanks will be. Then where the fresh water tank will be, where the city water will connect, where the water heater will be, and all the faucets and toilet. Once you have settled on a workable plan, then the building starts. It is a major project.
If your trailer had a toilet, the black tank is under it. Many old Airstreams had "rear baths" and the black tank is under the floor. Many old Airstreams had leaky windows and leaky plumbing causing the wood floor to rot out. The floor in my 66 Trade Wind was rotted and needed replacing before any plumbing could start. More work.
There are some good Overlander rebuild project threads you can stay up all night reading where you can learn how others have done it. Here is one that has it all...