Ukrainian Lacing is a technique that fixes all major problems of conventional shoe lacing with no tails, at the same time doing a knot remains habitual. You are welcome to watch the videos above (and below) to quickly get the main idea behind this technique before getting to the step-by-step instructions.
Step 1: Start Lacing From the Top Pair of Eyelets.
Step 2: Pass the Right (as Seen on Your Foot From Above) End of the Shoelace Through the Next Opposite Eyelet.
Step 3: Turn the Left End of the Shoelace Around the Other One From Above and Pass It Through the Next Opposite Eyelet Forming a Half-knot.
Step 4: Lace to the End With Any Preferable Style (e.g. Criss-cross As Shown) and Do Small Knots on the Ends of the Shoelace.
Step 5: Tighten and Arrange the Shoelace So That the Half-knot Is Located in the Second (not Top!) Pair of the Eyelets. Now the Ukrainian Lacing Is Ready.
Step 6: Before Doing a Knot Tighten the Lacing and Make the Loops Even (that's Very Easy).
Step 7: Do Any Preferable Knot, E.g. a Standard Knot As Shown. We Recommend the Ian Knot.
Step 8: The Knot Is Ready. No Tails at All! Neat and Well-looking.
Step 9: To Undo the Knot Just Pull Any Loose Segment of the Shoelace. You Can Also Comfortably Wear Your Footwear With Undone Knot When Using the Offered Technique.
Step 10: Practice and Experiment: Great Video From Dave Hax and Itty Bitty Pals, the T-Lace, Ian's Shoelace Site
DaveHax made one of the best videos (top in this step) about the Ukrainian Lacing so far. Check yourself.
Look, how the shoelace ends are fixed in the bottom pair of eyelets in the video. This is just one of SEVERAL ways of doing that. Another possible way - when fixing the shoelace ends in the bottom pair of eyelets you might try to pass it a second time through the OPPOSITE eyelet, not the same. Dave's way is great, but in some cases (e.g. a soft edge of the shoe, too long shoelaces, visual preferences) the above can also serve well. And, of course, you might tie the shoelace ends together with a neat knot of your choice or use a clip for the same purpose.
You might also prefer the T-Laces (shown on the picture above), though "no special shoelaces needed" approach seems to be nicer in some regard. BTW, I use knots as shown in the instruction above and have never felt them, though, sure, it depends on the particular shoes and shoelaces (very thick shoelaces might be a challenge in this regard indeed).
Moreover, you can omit the "fixation tricks" altogether and just leave the aglets behind the bottom eyelets if the eyelets are relatively small like it's shown in a nice video by Itty Bitty Pals (above). When the shoes are put on it's most unlikely that the aglets will slip out the eyelets in this case.
UPDATE: Ian Fieggen (author of the famous Ian Knot) has added a great tutorial about the Ukrainian Lacing to the best ever online shoe lacing encyclopedia, Ian's Shoelace Site: www.fieggen.com/shoelace/ukrainianlacing.htm
Step 11: Become a Shoelace Ninja Like Dave Hax
Words cannot tell that. Just watch how a combination of the Ukrainian Lacing and the Ian Knot is performed by the Master.