Basic syntax for graphing a function of two variables:

Plot3D[(1-t^2)*x+t^2,{x,0,1},{t,0,3}]

Including an option to lable the axes :

Plot3D[(1-t^2)*x+t^2,{x,0,1},{t,0,3},AxesLabel->{x,t,u}]

Basic syntax for a contour plot with a few options included:

ContourPlot[(1-t^2)*x+t^2,{x,0,1},{t,0,3},
Contours->10,
ContourShading->False,
ContourLabels->Automatic,
FrameLabel->{x,t}]

Back to plotting a graph of the function but this time with the contour curves on the surface.  This is accomplished with the MeshFunctions option.  The syntax for this option is less obvious than most Mathematica syntax.  Here, #3 refers to the third variable which the output variable.  In similar fashion, #1 refers to the first input variable (x in this case) while #2 refers to the second input variable ( t in this case).

Plot3D[(1-t^2)*x+t^2,{x,0,1},{t,0,3},
MeshFunctions->{#3&},
Mesh->10,
AxesLabel->{x,t,u}]