If you have a function that describes your curves then use Table to create the data points that you want. This might look like

ListLinePlot3D[{
  Table[{.01,y,1.Sin[y]},{y,0,2,.02}],
  Table[{.33,y,.5 Sin[y]},{y,0,2,.02}],
  Table[{.66,y,.3 Sin[y]},{y,0,2,.02}],
  Table[{.99,y,.2 Sin[y]},{y,0,2,.02}]},
  Boxed->False, Axes->True, PlotRange->{{0,1},{0,2},{0.2,1}}]

If instead you have a list of data points then replace each of those Table with your actual data with {x,y,z} for each data point.

That is then going to do four separate line plots for the four colored curves that you have.

If you need to tweak the style of the result then you can go wild with the hundreds of buttons and knobs and options and directives for the time you have to spend on this. Look up ListLinePlot in the help system, click on the orange Details and Options and study all the things that will let you do. Then you can search the help system for other words I used, like Boxed, Axes, PlotRange, Bold, etc. I suggest that you always save the last partly working copy that you have and make one tiny change at a time and decide whether to go forward or backward after each change.