Those of us who are out in the woods a lot are the most likely candidates to find archaeological remains. Knowing where to look and what to look for can help you to spot these things.
People have been living in New Hampshire for 12,000 years, and during the 11,500 years of prehistory they were living over and over again in the same preferred places: on river and lake shores, especially on river and lakeside terraces, at falls and at river deltas, inlets and outlets. Post-glacial nomadic hunters camped in these locations, hunter-gatherers preferred these spots for seasonal settlements, and village horticulturalists found this to be the best land for planting, so these locations often have layer upon layer of buried artifacts.
One other potential archaeological location is at or near outcrops of fine-grained stone, where people repeatedly came to quarry the stone, knock it into rough "blanks", and carry it away to finish tool-making nearby.
Of course these spots are likely to be covered with soil and trees, but wind and water may expose the artifacts. Where there is disturbance, look for pieces of fine-grained (smooth, slippery) stone. Look for signs of straight-line fracture or of chipping of the edges - these were tools or the debris from making and sharpening tools. You could be looking at something 12,000 years old. Look for pieces of pottery, often "stamped" with a raised pattern on the outside surface; this could be 3,000 years old. Also look for metal, often oxidized to green or another color - this could date from the time of contact and the fur trade.
In rare instances you may find wood, bones, birchbark and other organic material - usually in a wetland, and especially a peatland, environment. Again, draining or other disturbance is likely to reveal these things.
If you find something, there is probably more underneath, and the undisturbed stratigraphy is very important. So, mark the spot (but not too obviously), and don't dig! If you are on SPNHF land, notify Carrie or Dave Anderson. As the landowner, SPNHF will follow up with the Division of Historical Resources, and the site may be visited by archaeologists. There will not be much fanfare, because archaeological sites are fragile and sensitive to destruction by casual collectors. In fact, archaeological site information is exempt from the Freedom of Information Act for just this reason.
If you are on other land, notify the landowner, recommend contacting the Division of Historical Resources, and emphasize that an archaeological site does not affect a landowner's rights
in any way. If archaeologists are permitted to visit, they must follow the landowner's instructions, and if they excavate the site, they will restore it. In fact, they will do their best to make it look like nothing ever happened there.
There is also Historic Archaeology, so cellar holes, old dams, old dump sites, etc. are worth noting, marking, and notifying SPNHF. The same procedures apply.
Nine-tenths of archaeological sites are found by non-archaeologists and SPNHF stewards and staff are likely to find some.