How to accurately join two parts of an object

I´ve starting working on a model just to give some life to the design and to lern in the field how to use blender. I start modeling it using extruding, and works fine until I get to a place where I cant join the two parts without disruptin the geometry of the model.

I wonder If there is any way to move vertex in order not to go through other faces of the same object (like colide them) or any other approach that you would think it could be useful.

I´ve attached some images bout my problem so you can see in a more practical way. By the way sorry about my english, I could explain it further if it isn´t clear.


I need more explanation, sorry. Can you upload the blend? put it at pasteall if it is too big or cutout the parts you need and append them to a new file, or just explain some more. Are you trying to join two objects? Is it just one mesh? Are you trying to make faces?

Use Snap tool and choose Volume in the snapping constraint.