Can one tell which way the market goes from sell and buy orders? Among other open access (i.e. public) data available in exchange API's are the open order books. They are given on exchange websites sorted by coin value. Is there a way to tell which way the market is going, as in up or down for a given pair, from sell and buy order books? 
If the only way is by taking two snapshots of these data, would that be a good way to do it, or is there a better way, using public API's?
Market direction, as with any direction, only applies when you have more than a single data point.

So, the value of the trade at t-1 compared to the value of the trade at t can tell you if the market moved "up" or "down".  The value of t, by itself can only ever tell you the value of t.  There is no way to determine direction or velocity from a single point value.

If an individual API provides direction, then you could use that; however that is up to the individual API to provide.