Not sure how to set up the Laplacian/Poisson Equation

Something like this?

PDE = D[V[x, y], x, x] + D[V[x, y], y, y];

BCs = {DirichletCondition[V[x, y] == 0, y == 0], 
   DirichletCondition[V[x, y] == 1, y == 0.05], 
   DirichletCondition[V[x, y] == 0, x == 0], 
   DirichletCondition[V[x, y] == 0, x == 0.1]};

ufun = NDSolveValue[{PDE == 0, BCs}, V, {x, 0, 0.1}, {y, 0, 0.05}];

ContourPlot[ufun[x, y], {x, 0, 0.1}, {y, 0, 0.05}] 

For Poisson equation replace PDE == 0 by PDE == f[x,y], where f[x,y] is an arbitrary function.