Point the analog stick upwards slightly, or press it up and hold it while Link is occupied with another action that can't activate jump (the stick can be held up all the way in these circumstances).
Behold! Link's tilt game!
Trolling aside, Link's best way of winning is by hitting a bunch of up airs on the opponent or using his reasonable edgeguarding to gimp or rack damage after hitting the opponent offstage with one of his decent finishers. Often, the first bleeds into the second because of a bunch of reasons. So, coming back to tilts, his up tilt is a good move on its own. But the fact that it feeds his main strategies for winning and fills a bunch of important niches makes it one of his best moves. The move is sort of like his version of Sheik's f-tilt in a lot of respects, except it's just not that good.
F-tilt can be used for edgeguarding. Someone said it's safer on shield than f-smash but I don't find this too true in practice simply because the timing games you can play with f-smash (the window for Link to initiate the second swing is pretty sizable) creates a sort of "fake frame advantage" in that the threat of the second swing can discourage direct counterattacks on it (wavedash > grab OOS, for instance).
D-tilt is cute because it can set up dair in a bunch of ways but it's mostly for edgeguarding and crap. It's too slow to be useful for crouch-punishing, terrible vs shields if it doesn't pierce, and generally overshadowed by grab as a combo starter. So yeah.