This should be posted in “Basic&Interface” or “Modeling” of the help section ;D
Nonetheless, you can not merge vertices of seperate objects. the best you can to is to let them occupy the same space in your world, which isn´t really desireable.
We´ll fix that takes freaks hand
Be in object mode.
select both objects (shift+click)
press ctrl+j (oin)
then the two seperate meshes get one object and one editable mesh.
press tab to enter editmode.
select the two vertices and press ctrl+m (erge)
You´ll be asked to merge at center, first or last. selfexplainatory.
There is also the option to automerge vertices and use the snap option, this way you can just drag one vertex into another, but thats advanced editing
Start with a cube
add a plane
Shift select the cube and plane Hit ctrl + j to join the two objects.
so now when you select either object both objects will be selected.
If this is the case then you can enter edit mode and join vertices.
I think Arexma explained it quite well but you seemed to have missed the point that the two objects must be one object.