At each time step in your molecular simulation, you're updating the velocities and positions of your particles. If the updated position of one of your particles crosses a boundary, you can implement reflective boundary conditions by flipping the sign on the velocity component orthogonal to the boundary, as if the particle had undergone an elastic collision with a wall. For instance, if one particle is at x=0.1 moving with vx = -0.3, and I have a boundary at x=0, when I step forward in time (we'll say Delta t = 1) my new x-coordinate would be -0.2. This crosses my boundary, so I'll instead update the x-position to 0.2, and then change the x-velocity to +0.3. If you have difficulties with the implementation, just remember it's like an elastic collision and you can work out what the new position and velocity should be using classical mechanics.

In some instances, it may make more sense to use periodic boundary conditions, where a particle crossing one boundary is translated to the boundary on the other side of the simulation box. For instance, if our box runs from 0 to L in the x-direction, a particle at x=0.1 moving with vx=-0.3 would be placed at x= L - 0.2 when we update the coordinates- if a particle goes too far to the left, it reappears on the right edge, like Pac-man. For simulating adsorption onto a surface at z = 0, it would make most sense to me to use periodic conditions in x and y if your surface is uniform in those dimensions, and a reflective boundary condition in z.

From what I have seen, reflective boundary conditions are used to study the effect of finite-size on ensemble averages, simulating "caging" or other boundary effects.  There are a couple of different ways of setting this sort of simulation up.  As James said above one way is to simple reverse velocities at some defined simulation boundary.  The other way that I have seen is to use some sort of confining potential that affects all of the particles in the simulation.  Please see the following links for some examples.

http://www.tandfonline.com/doi/abs/10.1080/00268978800101661

http://pubs.rsc.org/-/content/articlelanding/1978/f2/f29787401532#!divAbstract

http://pubs.acs.org/doi/abs/10.1021/jp057532s?journalCode=jpcbfk

Thank you very much James and Jamin for the answers, I really appreciate your time! 

I also have another question, when is the confining potential preferred to the spatial reflective boundary? It seems there are errors associated to each, but how can one decide to use which? My question is based on this article:

http://iopscience.iop.org/article/10.1088/1742-6596/774/1/012148

Alizera,

I have tested a confining potential and compared it to periodic boundary conditions and I found reasonable convergence for bulk thermodynamic properties, but there were definite differences in energy transfer.  This was molecular dynamics and there could be differences in a purely Monte Carlo simulation.  The only way I think that there is to know is to do a side by side comparison.