The strongest terminal knot is the Six Turn San Diego jam, which wraps around both the line and the end of the line. When tying this knot, first thread the line through the hook, and then pull the end roughly ten inches from the hook.
Loop the end strand six times around the line and itself, moving closer and closer to the eye of the hook. When six loops have been completed, pass the end of the line through the opening in the line closest to the hook, and then thread the end through the loop at the top of the knot. Then pull the line tight, closing the knot. Be sure the loops stay in a spiral configuration and do not overlap. Lubrication may be necessary to properly close this knot and tighten it evenly.
To splice two lines together, use the Six Turn Yucatan knot. Begin by doubling up the lighter line and wrapping it around the heavier line for several turns. After this, simply pull the end of the heavier line through the loop created by the doubled up line and pull tight. Clip off any remaining extra line, but be sure to leave enough of the heavier line so the knot does not come undone. Lubrication may be useful when closing this knot as well.