Erect your fence as usual. You can paint the boards and posts with creosote before they are erected, but this procedure is messy and not as effective as painting the fence once it's complete.
Open the creosote bucket and dip a stiff-bristle paintbrush in the creosote. Wipe off the excess creosote on the rim of the bucket.
Paint the fence as you usually would, being careful not to drip the creosote on the ground. Make sure you cover all the spots and crevices. Let the creosote run into the parts where the fence meets the post so they are all treated.
Allow the fence to dry. Because creosote is an oily substance, this can take a few days, especially in damp conditions. If you are containing animals with the fence, you will want to check that it is dry before you allow them near the fence.