Assuming that woodworkers like to recycle material, I suppose this is on-topic. I'll let the community decide.
The key here is what is reusable, and what is not. At least for the weekend woodworker. A secondary concern is what to do with scrap that can't be reused.
I think the wood you will find falls into some general categories:
- Wood that can be reused, and can go in your scrap pile
- Wood that can be reused but might not be useful for indoor projects
- Wood that might be reused, but reusing it would be a giant pain, so might not be worth it
In general, the great majority of the wood you find will fall into (1). And (2) is easy to identify. This is the "pressure treated" variety of lumber for outside projects where rot is a concern. You should not use it for indoor projects, and when working with it some care should be taken to not overexpose yourself to the dust.
So, you have a pile of old wood and you want to decide what to do with it. First, separate it into three piles:
- Painted wood
- Unpainted wood
- Pressure treated or otherwise wood treated for outdoor use
If you have any of (3) and you want to keep it, stack it up and use if for outdoor projects. If you do not want it, the it should be taken to a municipal dump of some sort to be properly disposed of. The details of this will depend on how your local municipality disposes of "toxic" materials like batteries and petrochemicals. Do not burn it! Again, depending on your local laws, generally small pieces go into the garbage, and larger pieces can be brought to the dump (either by yourself, or if your city has a monthly "large item" pickup program).
Now you have piles of painted and unpainted wood. Ideally, you test the painted wood with cheap lead testers and determine which, if any, have lead-based paint. If any do, you have a decision to make: do you keep it or not. If you keep it, you have to use it a bit carefully. Ideally, you minimize any dust you make while it is painted. This usually means chemical stripping it down to bare wood. If you don't want to do this, it goes into the garbage or dump as if it was batteries or old fuel or any other toxic material. Do not burn it.
The rest of the wood is probably safe to use as-is, though as usual you should be wearing proper respiratory equipment when making any significant amount of dust from any wood. Some finishes have small amounts of metals added to help with drying, but these are very stable once cured. Again, use prudence when working with it.
However, it can be tough to distinguish actual pressure treated wood with wood that has been coated with a similar sort of material used in PT processes. In my experience, these finishes always have a lingering odour because they never really dry. They are usually oil-based penetrating finishes; they will look -- and smell -- different than most other finishes, including the less toxic penetrating finishes out there.
I'd advise not burning anything but the cleanest unfinished wood. But as long as it is not pressure treated, or contains heavy metals, it'll burn ok, but you have no way of knowing the details of the how the finish will react when combusted. Unless you have one of those super high heat wood furnaces, who knows what old finishes and embedded metals will do in the partial combustion present in most run of the mill fireplaces or furnaces. It would certainly be terrible in a backyard firepit. All you are doing is potentially dumping a lot of free-based chemicals into your local air.
That all being said, I used offcuts from a cedar siding project in my firepit, but this was seasoned western red cedar with no finish on it. Likewise for construction grade spruce or fir. But finished furniture? Save that for the apocalypse when you have no other choice.
Finally, when in doubt, just toss it. Wood is a renewable resource and, unless we are talking beautiful seasoned hardwood from wrecked but salvageable antique furniture, anything you find will be easily sourced somewhere else more dependably.