How to find useable parts for building the trailer you need.
Since you are reading this I have to assume you already have a trailer in mind. Now you simply need to decide what it needs to do and how big it needs to be! A small trailer is simple enough to build; there are a few things you need to know before you start.
Note: You need to be comfortable with your welding skill to build a trailer. If not, you will need to find someone who is; as a trailer is not something you want to have fall apart on you!
One of the easiest trailers to build starts with an old disabled pickup. There are trucks rusting away in back yards and in junkyards all over the country. I started with one that had already been made into a trailer, but it is easy enough if you have access to cutting torches and a welder to build one from a truck.
Once you have the truck, you need to be sure you can carry the weight you intend to carry. Get an estimated weight for the equipment or items you intend to haul so you can get an axle and springs that will carry it, breaking an axle on a loaded trailer is no fun and could end in tragedy.
If the original truck could carry the load safely, then the resulting trailer will too.
If you try to scratch build one you are going to end up with a lot more work, building a frame, centering the axles under the weight, getting everything connected properly so the trailer holds together and getting it to pull properly. There are size restrictions on our highways that must be met if you want to license it for the road as well as lighting and reflector requirements.
If you are going to haul a riding lawn mower it is simple enough to find axles that will haul one, hauling a heavy load is a totally different story.
Fining an axle, tires and wheels: I had to replace the axle to able to get replacement axle bearings and brake parts which also allowed newer tires and wheels. (Split rim wheels should always be replaced as they are dangerous!) Weight rated trailer tires were also a must since I needed to carry a lot of weight. Normal car or light truck tires will blow out if you over load them. I bought a straight axle from a mini-van and three wheels from a salvage yard pretty cheap.
I also had to change over to load rated trailer springs I purchased from a spring shop. The old pickup springs were far too soft and caused the trailer to bounce and become unstable, even without a load. Shocks were left off with little effect on the trailers tow-ability, but that was alright for my needs. Instant improvement in towing and handling!
Starting with an entire truck you would need to strip it down to the frame and measure carefully before cutting the front end off, leaving enough frame rail to notch and bend in to form a hitch head. The frame ends have to be equal and centered, or your trailer will pull off center. Also leave the wiring long enough to be tied into the hitch harness plug of the tow vehicle.
Hitches are also weight rated and must be matched to the load you intend to pull and the tongue weight you will have. Tongue weight is very important to the trailers ability to handle and if overloaded it may disconnect or break off leaving you towing your precious cargo on safety chains, hoping to make it safely to the side of the road. I would strongly suggest investing in a receiver hitch, bumper hitches have a very low weight rate and it is entirely possible to break the bumper off with overloading.
Safety chains must be added by law and must be able to hold the trailer in a disconnect situation. They must be long enough to allow turns, yet short enough not to drag the ground.
Lights and wiring can be purchased at most large department stores cheaply or at your local auto parts store. Follow the directions provided and be sure the harness is left long enough to reach the tow vehicle with out dragging and still long enough to survive turning.
Brakes can also be important if carrying extra weight! Your tow vehicle can have brake failure if severely overworked, or its brakes may not be able to effectively stop you even in normal situations since they are not designed to stop the extra weight. Brakes for trailers can be electric or hitch actuated, coming on when stopping exerts pressure on the hitch.
I started with an old pickup utility box trailer with a ladder rack, and ended up with a heavy duty enclosed trailer, carrying up to 3500 lbs of cargo, safely and out of the weather. That trailer has been back and forth between Colorado and Florida numerous times.