How can I calculate the cyclic (periodic) convolution?
People generally define the cyclic convolution of periodic sequences
$x$ and $h$ of period $N$ as
$$y[n] = \sum_{m=0}^{N-1}x[m]h[n-m], n = 0, 1, \ldots, N-1.\tag{1}$$
Note that the above expression consists of $N$ different sums that
you have to compute, and if while computing any particular sum,
the value of $n-m$ is not in the range of numbers for which you
are given $h[\cdot]$, then you use the periodicity ($h[n-m] = h[n-m+N]$
or $h[n-m] = h[n-m-N]$) to get the argument into the range for which 
you know the value of $h[\cdot]$. 
Also, note that $(1)$ holds for all integers $n$, but we don't
need to calculate more than $N$ sums like $(1)$ because
$y[n]$ is also a periodic sequence of period $N$ and so we have
for any integer
$M$ that  $y[M] = y[M \bmod N]$ where, of course, $0 \leq M \bmod N \leq N-1$.

Exercise: write out the above formula explicitly, meaning
no summations, for $n = 0, 1, 2$ and proceed from there.  Go on;
you can do it. There are only three sums of three terms each.