How do I generate a unit impulse signal in MATLAB?

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An impulse δ[n] in discrete systems is just a sequence of zeros except at n=0, where its value is 1. It can easily be represented by a vector (or array) in MATLAB.

A continuous impulse δ(t) is a distribution, or generalized function, and it is (in theory) impossible represent it exactly in practice. You can approximate δ(t) with any finite duration pulse with an area equal to 1. The simplest example is a rectangular pulse with width equal to ϵ and height equal to 1/ϵ. To use it in a system, though, you have to set ϵ to a value quite smaller than the shorter time constant of the system where the impulse is being applied. So you need to have some information about the system. Below are examples of several rectangular approximations to an impulse.

Going back to MATLAB, it happens that often you don’t need to create an impulse yourself, because there is an impulse() function which calculates directly the impulse response of a system. See its page, with examples, in Impulse response plot of dynamic system; impulse response data.