How can you tell when something STOPS touching another object?

Adding on to Goulstem's response, that would not work as expected if another part touches and stops touching the part, it will act as if the original part has stopped touching it. This is what I would do.

db = false

script.Parent.Touched:connect(function(hit)
    if db == false then db = true end
    if hit.Parent:FindFirstChild("Humanoid") ~= nil then
        before = tick()
        local c
        c = script.Parent.TouchEnded:connect(function(hit2)
            if hit2 == hit then
                tm = math.floor(tick() - before)
                print("Player was touching part for "..tm.." seconds!")
                c:disconnect()
            end
        end)
    end
    db = false
end)

The TouchEnded Event does that.

So to do what you want;

db = false

script.Parent.Touched:connect(function(hit)
    if db == false then db = true end
    if hit.Parent:FindFirstChild("Humanoid") ~= nil then
        before = tick()
        script.Parent.TouchEnded:wait()
        after = tick()
        tm = math.floor(after - before)
        print("Player was touching part for "..tm.." seconds!")
    end
    db = false
end)

-Goulstem