In sketchup you can move an object based on two points. This makes it very easy to align a vertex in one object to vertex in another object. Here is an example:
I want to know how to do this in Blender. It seems that Translate can't align vertexs
I don't think there is such feature, but you can achieve precision with numbers.
Say i have a cube the size of 1, 3, 1; and a cube with the size of 1,1,1. In the objects menu, you have the exact location of an object, so if I wanted to add the cube on the y axis (similarly to how you did it), you can make the location 4 (3 + 1).
However if you want to join the objects as you would when building a structure, you can use the extrude function to duplicate vertices, and move them. You can also use loop cuts to help.
As you can see, there is an edge line through the middle, that was done with the loop cut. I selected the verticies I wanted to "duplicate", I pressed the E button, and moved them out. You can press the X, Y, or Z key to move verticies on one axis
While in Edit mode, change the snap to Vertices and select Active option. As stated by the Blender referece manual's page the snap target options:
determine what part of the selection snaps to the target objects.
In particular the Active option:
move the active element (vertex in Edit mode, object in Object mode) to the target.
Select the geometry to move and set the wanted vertex as active (should become white instead of orange).
Now you can use the active selection as pivot point to snap the selected geometry around.
Another method could be to move the origin of the object to a specific 3D cursor location and use it as your pivot point. In object mode, Active option is infact referring to the origin of the active (bright orange) object of the selection (dark orange)
Both methods above are quite fast, but they both have the disadvantage of messing up your initial object origin's location.
If you are interested in keeping the orign in it's relative coordinates from the geometry, I would suggest to use a third "dummy" object that would be your temporary pivot and delete it when the trasformation is over. You can use for example the Hook to new object command to quickly create an empty upon the selected geometry.
One other alternative to what is already present here is using the third party addon NP Station
Among other features It provide a transform workflow similar to what Sketchup and CAD like applications provide, specifying a base point and a target, or even three point alignment.
It also provides dynamic viewport tooltips with a HUD like UI