Q:

How to determine drainage area upstream from point?

I do not know how to come up with the drainage area (km squared) upstream of Lat 77.84, Long -30.96. I have converted my contour shapefile to a raster, identified and filled the sinks and then created a flow direction raster, but after that I am not sure what steps to take.
I can create flow accumulation, but none of this is showing me where to insert my lat and long point to get the drainage area upstream from that point. I have all the hydrology tools, but do not know what to input to get the correct answer. I am a newbie.
I have tried watershed/subwatershed delineation. The results I got were very small areas adjacent to my points. What I need is the whole upstream area that contributes water to that point. 

A:

The flow accumulation is the right tool for you, after as mentioned filling sinks (fill tool) and create a flow direction raster.
"The Flow Accumulation tool calculates accumulated flow as the accumulated weight of all cells flowing into each downslope cell in the output raster. If no weight raster is provided, a weight of 1 is applied to each cell, and the value of cells in the output raster is the number of cells that flow into each cell."
That is, each cell in a flow accumulation raster with no weights applied, stands for the number of upstream cells that flow into one downstream cell. All you have to do is create a point feature in the desired lat / lon and extract raster values to point, than multiply it by raster cell area. 
For example - attached image shows the point that was digitized as a destination for upstream drainage area calculation. I used raster resolution of about 30.8 Meters to compute the area of a cell; and used extract values to points tool to get the flow accumulation value at my selected point.

Than the field calcultor expression was: 

[RASTERVALU] *0.03081888914^2

