You can use the merge edge tool to combine the edges of polygonal objects in order to form one solid object.

It is important to have the same number of spans on both objects.  Notice how all of the horizontal lines on both models line up.

Below is a screenshot of two separate polyonal objects that I want to merge together:

Notice that both objects are selected.  The first thing we need to do is combine these objects.  So with both objects selected do Edit Polygons>Combine.

You now have one polygonal object instead of two.  It is not possible to merge the edges of two seperate polygons.  You MUST combine them first.

Now grab the merge edge tool.  It is located at Edit Polygons>Merge Edge Tool.  Then click and hold with the RMB to bring up the marking menu.
From the marking menu release on Edge.
Click on one of the edges.  It should now look like this:

Next click on the opposite edge:

From here you can either hit the enter key and the edges will merge, or you can click on the next edge.
In this situation I want to merge all the edges going all the way around my object so I am going to click on the first edge in the next set of edges.

And then on the edge I want to merge with the selected edge...

In the next screenshot I have numbered the edges in the order I clicked on them:

Just continue in this pattern the whole way around the object.
 

more Maya tutorials
comments..suggestions..questions:  josh@occipital.net
the rest of my site is here: http://www.occipital.net