Your snapping options are on your status line.
And the toggles are as followed:
x- Grid snap
V-point / vert snap (also snaps to transforms cameras, joints etc.
c- Curve or edge snap (will snap pivot of current selection to point along a curve or edge, does not snap an edge to another edge uniformly, you will see what I mean)

to snap your objects together, select what you want to snap hold down one of the snap toggles (you probably want point snap to snap from vert to vert) and middle mouse click drag over the vertecy you want to snap to.

To merge the objects just select the various objects and go to polygons>combine. Then to merge the verticies together select the new combined object and click merge vertices ( if you find you get weird results go to the options for the tool and change the threshold).

Make sure you go into faces and delete the internal faces otherwise you will get problems.

Then to soften the object up go to normals> soften edge or set normal angle.