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If you have a map (hotspot or other) that has gps grids on it and you find a spot that does not have gps coordinates already listed. Is there a tool you can use to determine those coordinates? How accurate will it be?

That is fairly simple. What you need is a ruler, and divider, pencil, paper, and some other simple tools. Mariners have been navigating this way for centuries.

LatLon format are usually in DDD.MM.SS, or DDD.MM.MMM.

1 degree = 60 minutes
1 minute = 60 seconds

Also, 1 minute = 1 nautical mile, well, kind of. Depending on if you are figuring out lat or lon, and how close you are to the equator or the poles. But you said you would be using a map that already has latlon markings on them, so you will just divide it into smaller increments, and that should be sufficient.

Now, I am not a mapmaker, and I am not someone who knows every little bit of mapping details. However, I know it well enough for me to get to where I want to go, to navigate from country to country, use a sextant to take a sun sight to obtain my position in the middle of the ocean, able to sail across the Pacific ocean, and not miss arriving at a landfall on some small island or atoll, or sail up the inside passage from Seattle to Alaska. For me, that is accurate enough. Of course, I am always working with updated navigation charts. By the way, if on land, charts are called maps.

So, as for your accuracy, how accurate do you want to be? Down to feet or inches, or mm? Or just close enough is sufficient. Mathematically, you can get as close as you want to be, but you will also need a good thorough understanding on mapmaking, and how the earth is measured using latlon.