Remove any suckers growing from below the bud union; such suckers will not produce the fruit you expect and will tend to make the rest of the tree weaker over time. Such suckers can be removed at any time of year, as soon as you notice them.
Make the pruning cuts as close to a lateral branch as possible. Let pruning wounds dry out naturally without sealants or dressings. Pruning should be done cautiously, since an abundance of foliage is necessary for a good yield and to protect the trunk and branches from sunburn. Remove as little green wood and green leaves as possible. Prune only after the tree has sufficient upper foliage to prevent sunburn. Avoid pruning in late summer and early fall, to avoid stimulating vegetative growth.
Read more about pruning avocado trees.