Shulk's only real bread-and-butter combo is landing N-Air into Jab/D-Tilt/F-Tilt or Grab (I like to go for the Grab), and these don't always work consistently. He has a few very situational things here and there, but he's not a combo character at all, so just focus on his neutral as you start out.
As it's been mentioned, though, Shulk has a good time getting into good positions that are very close to true combos, so instead, you just have to get a good rhythm going and confuse the opponent between going for the links, or predicting/covering their dodges and evasive options.
Some examples:
D-Throw to a quick dash and F-Air. (Works best and to much later percents with Speed)
U-Throw into U-Tilt, or at high percents, (Monado boosted) Jump into U-Air.
F-Air positions into itself with Monado Jump, even true combos at some point as stated above.
D-Tilt into F-Air
Keep in mind attacks used with Buster at lower percents will keep the enemy very close to Shulk, so experiment around with that (but be careful, the lower hitstun can actually get you punished even on-hit with certain attacks).
Not much of that is really true combos... but they will hit an enemy who doesn't react quickly, and they can't be simply jumped away from in a lot of cases, which you means you can really mess around with punishing air dodges and stuff.
Really though, his N-air is pretty amazing.. In Speed, N-Air > Grab > D-Throw > F-Air is pretty reliable, though the F-Air is avoidable, it will force them to land with dodge lag... then you can regrab, F-Smash etc.. I guess in a nutshell, Shulk excels at making his own combos by forcing the enemy into disadvantageous positions, and you need good foresight (or clairvoyance) to play against how enemies react to you, but his flow and range makes it fairly easier than most other characters.
