Here is a manual method using copy-and-paste that is suitable for small volumes of data on an ad hoc basis...
1) Enter the following expression into a notebook, but don't evaluate it:
data = ImportString["", "TSV"]
2) Copy the cells from the source spreadsheet onto the clipboard.
3) Paste the contents of the clipboard between the empty pair of quotes in the expression from 1). If Mathematica brings up a dialog asking whether you want "escapes inserted", select Yes. The result should look something like this:
data = ImportString["1.0\t2.0\t3.0
0.4\t0.5\t0.6
7.0\t8.0\t9.0
","TSV"]
4) Press SHIFT-ENTER to evaluate the expression.
5) data
now contains the pasted cell data, interpreted as Tab-Separated Values (TSV).
Alternate Approach
Follows steps 1) through 3) as before, then...
4a) Triple-click on ImportString
in the expression from 1).
5a) Press CTRL-SHIFT-ENTER to evaluate the highlighted expression in place.
6a) The notebook now contains an expression that looks like this:
data = {{1., 2., 3.}, {0.4, 0.5, 0.6}, {7., 8., 9.}}
... but that expression has not been evaluated yet.