It depends on the forecast I am trying to produce and what the weather is looking to provide, but for the average forecast text and graphics I do for this site, probably a solid hour of looking at data. If there is not much to forecast for, it can be as little as 20 minutes. If there is a lot, I can spend 1-2 hours looking at all the data.
As for the accuracy, that also will vary. Sometimes the models are in the groove and I can have a fairly reliable feeling about things 7 days out. Sometimes the forecast for the next 24 hours is totally up for grabs! It just depends on the situation and how the models have been performing recently.
Computers have always done the calculations for the forecast models. There are millions of calculations to be made and by the time any team of humans got around to doing the computing by hand, the weather they would be trying to produce a forecast for would have happened a month ago!
What is still done 100% by human is the interpretation of the model data. It is never 100% right and many times there are differences of opinion amongst the models and it takes a human to try and draw conclusions and a consensus from all of those options.
That is why weather forecasting is both an art and a science.
-John