One approach is to make use of the Cell options CellFrame and CellMargins to build up the frame around multiple cells using partial frames around the set of cells.  Using CellFrame, the first cell has frame elements at the top and sides. The inside cells have frame elements around the sides only.  And the bottom has frame elements on the sides and the bottom. Then using CellMargins the vertical distances between the cells is made 0 so that they abutt.  Here is a programmatic example, but you can use the option inspector to make these changes interactively.  Also one cold write a function that does this for a selection of cells and then put that function into a button and then into a palette if one wished.  (Tweaking this all so it works in a more general case requires also playing with CellFrameMargins option settings. This is just a quick proof of concept example...)

Realizing that you are new to Mathematica, this may seem pretty complex. If I have some time later on I can put together a one-button Palette that can do this for you.

I am not sure, though I did understand that that was your hope -- modifying a top-level cell in a cellgroup structure to draw a frame around all that are in that cell's purview. Generally this is not possible in this way though I am sure that I could come up with some invention that made it look like it worked ;-)  

The problem is that generally a given cell does not have knowledge of other cells in the notebook in that sort of dynamic fashion.   And the low-level  function that does know if cells are grouped, CellGroupData, has no options. 

Here are two discussions of this on Mathematica StackExchange (the first referring to the second) which don't get much further conceptually than what I was originally suggesting.

http://mathematica.stackexchange.com/questions/29475/is-it-possible-to-frame-a-group-of-cells
http://mathematica.stackexchange.com/questions/6264/automatically-use-inputonly-style

Clearly Mathematica should be able to do things like this. 

If you do not have any inputs in your content that need to be executed, then you might be able to do what you want within a single cell by putting the material in a Framed or a Panel like in the following.

Perhaps I will come up with some other ideas...