Pit is such an underused character.
You can ftilt lock him. You can run fast. You can shield from your dash relatively quickly. You can edgeguard. I don't see how this matchup could even be argued against Sheik's favor.
Anyway, Pit's arrows can easily be shielded, but they still prove a nuisance and give him initiative if he reads your movement well enough. Your options are to run in with shield, walk in with shield, jump over the arrows, or disrupt with needles (only if you started first; trading needles for arrows is a losing trade for you).
His greatest asset will be his clear advantage with disjointed hitboxes - you are never going to beat his uair, his fair and bair have a bit of startup but outrange most of your options, and the only way you can challenge his nair is with a maximum range fair (it has a bit of an invisible disjoint). His aerial mobility isn't as strong as G&W's or Marth's, but it still lets him play a relatively safe zoning game with them as long as he keeps you locked in shieldstun. If for some reason he lands right in front of you though, go ahead and punish from shield.
As I mentioned above, Sheik can ftilt lock Pit. However, ftilting shield is risky because of the speed and range of his fsmash. If you connect with a shield, instead of ftilting again, jab cancel to cover any poke attempts. In terms of killing, Pit is a medium-weight and has mediocre vertical momentum canceling.
Pit has too many options in the air for you to effectively juggle him from dthrow setups, so just run fthrow/bthrow and punish improper DI as appropriate.
Pit's Wings of Icarus is a horribly vulnerable recovery and is typically only used as a last resort, since getting hit out of it means he can't use it again until grabbing a ledge or landing somewhere. If he uses his Up+B stupidly, you have all sorts of punishment options available with needles, chain, and aerials. Don't count on this happening against any decent level Pits, though.
Don't spotdodge or roll into Pit. It can only lead to bad news.