The easiest way to accomplish the goal is to download Winboard with its own engine. The GUI can be set to output the current evaluation. You can recode the eval function to your own parameters.
http://chessprogramming.wikispaces.com/Evaluation provides some resources about programming the eval function. However, getting a well-documented source code for the eval function I find easier. Avoid the higher engines like Crafty, but a simple one like http://www.tckerrigan.com/Chess/TSCP/ is easy to understand.
Winboard is the best option, but you can create your own interface. You could modify a PGN viewer to return an eval after every move or put the FENs into a PGN file and loop through all games. You could download https://www-lucaschess.rhcloud.com/ or another chess interface which can analyse a game and use its output.
For the actual question, the chess eval is broken up into many factors.
The easiest is material: just loop over the board and count the material.
Next is pawn structure. Assign a penalty to isolated and doubled pawns. A bonus for passed pawns. (Pawns near the king is under king threats.) This can be modified further by changing the penalty based on the distance from the center.
Next is the pieces in relation to the pawns. A bonus for a rook on a open or half-open file. A bonus for a bishop which isn't trapped behind its own pawns.
Next is the pieces in relation to the center. The closer to the center the piece is, the more it is worth. This also includes a bonus for a rook on the seventh rank. (Trapping the king would improve this score, but this would fall under king safety.)
There is a bonus for having a bishop pair and the values of the minor pieces (the bishops and the knights) are adjusted based upon how closed the center is. A bonus can be added for more mobility (either absolute or for each piece) and/or space control. (Concentrated force(s) is a factor normally reserved for mating threats.)
This is a short list.