I learned to splice in the Sea Explorer Scouts, BSA. When I worked on the tugs the last 2 summers in high school, I taught the regulars how to splice. I use the eye splice for all my anchor lines with the metallic eye sleeve. Main thing in keeping your splice looking good is to keep it tight and keep twisting your individual (3) strands to keep them all together and tight then every time you make a round, tighten it all up.
No doubt www has instructions on how to do it. The main thing to get right is the 3rd strand which you turn the work over and reach across from the rear, catch that lonely strand looking right at you and tuck back under it. Once you get the first lay, the rest is just repetition.
HTH,
Mark