I have found a few old tools from the 1800s that have the date the patent was issued on them, but not the number of the patent itself. I have tried using the US patent office's website to find out more but have been stumped on how to navigate it. Does anyone have advice for how to look these up?
Try the following directory, which was created for people to look for patents for old tools: http://www.datamp.org/index.php
The USPTO database is only fully searchable for patents issued from 1976 on. You can only search by patent number or classification before 1976.
Also, there was a fire in December, 1836, that essentially resulted in the destruction of all of the records in the patent office at that time. Under the Patent Act of 1837, inventors could refile certain kinds of copies of patent document - those patents were numbered with an 'X'. So if you see a patent number with an X, it means it is from before the fire; if you want to see the image of an X patent on the USPTO website (once you have the number), you have to search with the format X#######, with the leading #s as 0s (must be 8 characters total).
(image search site: http://patft.uspto.gov/netahtml/PTO/patimg.htm)
Don't use the USPTO's site; it's a terrible website, just garbage. Instead, use Google's Patent Search (I know it looks just like Google's normal site, but it's not). It indexes material that the USPTO doesn't have and lets you specify many more filters for searching (click "tools" once you have some results) — including the date of patent issue. It's much easier to use. It sometimes has OCR errors but you can do so much more, so much quicker, using it.