We recall that

`csc\ x=1/(sin\ x)`

So we will have asymptotes where `sin x` has value zero, that is:

x = ..., -3π, -π, 0, π, 2π, 3π, 5π, ...

We draw the graph of y = sin x first, and consider the reciprocals of the y-values:

The graph of y = csc x: