When you get the hang of it, eye splices are relatively easy; you just need the right tools for the job. Fids are essential, but ridiculously overpriced. New England ropes has a great chart detailing the appropriate "fid lengths," which vary depending on the size line you're using. Bill used the measurements (and diameters we found online) to make me several fids out of aluminum knitting needles. They were a huge savings, and since they come in pairs I was able to use one as a fid, and the uncut needles served as the "pushers" needed to push the fid and line through the splice.
Once you have all of the tools, you start by measuring one "fid" length on the end of your line. This will be the amount of cover that eventually gets inserted back into the line.
Next you determine the size eye you want to make, and make a second mark. In this case it was dictated by the size of the thimble. Move up the line about 5-6 more fid lengths, and tie a jamming knot. Then go back to your second mark and extract the core from the cover.
Hold on to the core and "milk" the cover towards your jamming knot and back again a few times to "equalize" the lines. Your core should now be a bit longer than the cover. Make one mark on the core where it now exits the cover. Pull more of the core out and make a mark one short fid from the initial mark. Then another mark 1 1/2 fid lengths further down the line.
To make a more streamlined splice, you should taper the cover before feeding it into the core. Extract a few strands every inch or so from your first mark down towards the end of the line and cut them flush with the cover. IF you are adding a shackle, this is also the time to slide it on the core -- it will be too late after this point.
Now, insert your fid into the core at the short fid mark, and feed it through until it exits from your third mark. Put your cover end into the fid and use a "pusher" to move the fid and cover through the core. Tie a small knot at the end of the cover so it doesn't go back in while you're working on the next step.
Feeding the core into the cover is a bit trickier, since it will be a tight fit towards the end of the splice and if you force it too much, it will bunch up an seize. Insert your fid into the core at your first mark, and feed it through, past the point where you originally extracted the core and keep going about a short fid length. If it gets to tight, pull more core out. This also helps ensure you didn't snag any lines along the way. Put the end of the core inside the fid and use your pusher to move the fid and core through the cover. Once it's through, pull it tightly to remove any bunching at the "cross-over" (essentially the juncture where the cover and core meet). Hold on to the cross-over and smooth the line out.
Taper the ends of both the cover and the core so they essentially disappear back into your splice.
Your splice is now essentially done, except it's a bit oversized and you need to milk the cover back over itself to close your splice. Find something secure (a winch, a fence post, etc.) and belay your jamming knot to it. Hold firmly on your splice and milk the cover back, keeping tension on your splice the entire time. IF you're using a thimble, make sure you put it in spot before the eye closes too much. Milk slowly, being careful not to bunch up the line. Give it a few tugs, snaps, bends, etc. until the core moves all the way around the eye. The bigger the line, the more tension, tugs and muscle you'll need to get the job done, but in the end, you'll have a great looking eye splice that maintains the full strength of the line!