The first thing you should always try is using substition to evaluate limits. This is an example of a limit that can be evaluated with substitution.
What it looks like when the limit does not exist.
Sometimes substitution results in an indeterminant form. In that case, try factoring.
Indeterminant forms require more work. This video shows difference of two squares and using conjugate pairs to resolve an inderterminant form.
Examines the four limits above as a graph or a table.