Add noise to an example set
In addition to what Lupacante conceptually and nicely showed such that the added feature(s) has(have) to be informative for the model otherwise it can get ignored by majority of models (perhaps easily by regularized models), I would like add that you also increase the dimensionally of the feature space synthetically using many simple mathematical expressions as well. Concertedly, let's say your only feature (column) is: 

x

You may easily construct other features like (it is common practice actually in physical sciences):

x$^2$, x$^3$, x$^{0.5}$, $sin(x)$, x$^2$sin(x),...

Till you hit the so-called the curse of dimensionality for your exercise. Although I am not yet sure what features/num_samples ratio exactly causes the curse of dimensionality! What I have gathered so far about the curse of dimensionality has been very subjective.