Welcome to the boards! I am also a Sheilda main, and I would be happy to share what I know (but don't trust all of it over your own judgement).
E.C.H.O. covered a lot of the good stuff. I'll try to summarize and emphasize the most important parts, which will hopefully help you remember them during a match.
1) If the MU is better, switch when you get a chance. Sheik has a vaguely even MU spread, while Zelda has some she does well in and some she sucks in. You can find detailed discussions on these in the respective sub-forums.
2) If your opponent gets used to one, switch it up to confuse them. Related to this is whether or not the opponent plays Melee, in which case they start out used to Sheik.
3) Zelda is difficult to combo but easy to kill, while Sheik is the opposite. Consider starting stocks as Zelda and switching to Sheik around 65-95%, depending on the map and when you get a safe chance. After 135% Sheik will die on most stages anyway, so you may wish to switch back to Zelda so you don't spend time when you spawn.
4) Zelda racks up damage quickly while Sheik has the great neutral game for when you only need or can't afford one hit.
5) Counterpicking in tournaments. If the opponent doesn't know you play Sheilda, it is easy to bait bad stage selections from them. Sheik doesn't really care where she goes, but Zelda excels on tiny or huge stages, depending on the MU (leaning towards small).
6) Edgeguarding/recovery scenarios. Zelda can edgeguard certain recoveries well with a Din and lightning kicks. The ones she does poorly with Sheik still does well with. Transforming Sheik->Zelda can give you extra teleport distance and reduced endlag, but the load time should make you fall a bit first, so you can only use this when Sheik's recovery would still make it but will be punished (so, above the stage or close-ish). Transforming Zelda->Sheik can give you an odd burst of horizontal momentum while transforming, which allows it to be used as a recovery. Jumping or fastfalling before transforming then moving sideways should do it. I just kinda do it, so hopefully that's the right input...
7) Which times are safe to transform?
- opponent dead
- respawn invulnerability
- opponent far from stage
- Zelda/Sheik far from stage
- large stage (Dreamland, Norfair, maybe FD) vs campy player or slow character on the other side
- no way to recover, want to transform before death to save time later
- huge Dins explosion covers your transform. This works because Din explodes on transform
And I think that covers most things that are Sheilda-specific, and not just "how to Sheik" or "how to Zelda". Oh wait.
8) STYLE ON SOME FOOLS! Yeah this isn't my MO, but it causes massive hype when I'm either a) losing horribly and bring it back due to character swap or b) do crazy shenanigans with both characters or c) swap for just the kill move (Note: singular) and then switch back, usually due to an accidental downB lol the disrespect. Any of these can really get into your opponent's head, even if you don't mean to disrespect them. I know most of my opponents hate my Zelda, so if I ever play on point with Sheik too they just crumble and crack like a salt flat.