When is the best time to propagate loganberries?

The easiest way is to layer the tips of the shoots (snoots) after fruiting.

Peg the tip of a stem into the soil beside the main plant and it will root within a few weeks.

When rooted sever the rooted section from the parent plant and plant it in its permanent quarters.

Alternatively root the plant into a pot of gritty compost, rather than into the soil.

My loganberry has made masses of new growth this summer, can you tell me when and how to prune it?

Loganberries fruit on the previous year's canes

Prune your loganberry as soon as the leaves fall.

Cut out the old canes that have carried fruit this year to ground level, and also any weak /  thin ones.

Retain only the strongest of the new canes made this summer.

Tie the new canes into place neatly as a fan, and they should fruit next summer.