Few important notes about the implementation of the program in Mathematica:
(If I am incorrect, so please correct me)

1.  There is a requirement for installation of Mathematica or Mathematica Player Pro or webMathematica (Mathematica included).  Each of these programs are also licensed and charged. This means that the code will be able to use only the Mathematica owner with all restrictions. Second possibility is to make a web interface on your server with your webMathematica installation (licensed too).
2. There are no a full compiler to compile code independent of Mathematica. There are only commercial compilers with an uncertain outcome and equally dependent on the   Mathematica kernel. MATLAB has a compiler for stand alone applications but it is additional part (expensive).

If the preceding information does not mind role I would split task into several parts:

1.  Functions with “Module” with calculation part.
2.  Part for presentation – see: ”guide/ClickInteractivePanels”, “guide/CustomInterfaceConstruction”. It is commands for example: Panel,InputField,GraphicsGrid,Graphics,Button. Very important is command Dynamics necessary for program (variable) evaluation immediately after changing values.Button object can be used for starting evaluation (calling working Module). Very important is if you use very time constraining module or code then change default Option  Method->"Preemptive" to the  Method->"Queued" because if not your code will be aborted after some times and you will be without results.
3. Functions for importing and exporting results from/into program. This functions are called by buttons. Nifty command is SystemDialogInput["FileOpen"].

It was general description.

More knowledgeable user might write:
Make your own Mathematica package just for your own calculation.
For export/import data use Java Form or use some link: J-Link, MathLink ....

I apologize for bad English.

Well just going through some of the demonstrations, I see it is quite simple to enter a function and a range of variables and use Manipulate to create an interactive app with a slider to show the outputs on a graph. I would like my final product to be similar. I have several functions to solve for variables sequentially given 3 independent variables (namely, dry and wet bulb temperatures and atmospheric pressure to give Dew point temperature, humidity, vapor pressure, enthalpy, etc.). Generally, I think it would look like this: starting variables are x, y, z. f(x) and f(y) give variables a and b to be plugged into the next equation relating all three such as g(a,b,z)=w which is humidity. w is then used in the next equation to give another output and so on. I envision a program where I can enter these values of x, y, and z and be given the outputs that follow. Function 2 of the online calculator found at http://www.psychrometric-calculator.com/HumidAirWeb.aspx is basically what I want it to do. I could probably do these calculations easily using a simple excel spreadsheet, but my instructor wants a simple user-friendly interface using Labview or Matlab. I know very little about Labview, matlab, or mathematica, but when I came along mathematica it seemed like something I could do this on and also learn to do some very powerful calculations as I became more familiar with it. Any advice in the right direction would be much appreciated! Thanks!

It looks like someone has put in something like this already in wolframalpha as well: http://www.wolframalpha.com/input/?i=psychrometric+properties