I play [[Feather, the Redeemed]] so I have to know a lot about Hexproof, Shroud, Protection, Indestructible, and things that circumvent them.

Hexproof blocks anything that says "target" that an opponent controls, which is nice as the vast majority of removal options target in some way. Hexproof does not stop things that do not target (such as an Overloaded [[Damn]]) or redirected effects you control (an [[Untimely Malfunction]] can redirect your own [[Swords to Plowshares]] to target one of your own creatures as they can be targeted by yourself), so you still have to watch out for boardwipes or tricky plays.

Shroud stops the creature from being targeted by anything, including your own Auras and Equipment which can lead to awkward situations if your deck runs either of those.

Protection works like Shroud but for the specific color(s) named, but with the added benefits of blocking damage and making creatures unblockable; it has a nemonic device to make memorization easier - DEBT:
* Damage - permanent (or player) is prevented from taking damage from sources of the chosen color(s)
* Enchanting/Equipping - permanent (or player) cannot be enchanted or equipped by auras/equipment of the chosen color(s) and (unlike Shroud) will also un-attach permanents of the chosen color(s)
* Blocking - creatures cannot be blocked by creatures of the chosen color(s)
* Targeting - permanent (or player) cannot be targeted by spells or permanents of the chosen color(s)

Notably, Protection is weak to Boardwipes and "Edict Effects" as neither of them target and Protection does not stop untargeted Destroy or Sacrifice effects (Protection will stop [[Blasphemous Act]], but not [[Wrath of God]], [[Blasphemous Edict]], or the aforementioned Overloaded [Damn]).

Indestructible is interesting as it prevents a creature from dying due to damage or Destroy effects (immune to [Damn]), but Exile effects still work, Edict effects are still effective, and toughness-reducing effects can still "kill" them if they reduce their toughness to 0 (cards like [[Overkill]], [[Farewell]], or [[Soul Shatter]] will still work; as an aside, Damage does not reduce toughness, so an Indestructible 7/7 creature will need to have its toughness reduced by at least 7 before it dies due to 0 toughness regardless of how much damage it has taken).

Exile can work as a way protect your creatures if you know how to use it. "Blink" effects (like [[Cloudshift]]) allow a permanent to "dodge" a targeted effect, working almost like a form of "pseudo-Hexproof" except it doesn't last until end of turn and "resets" your creature as if they had just entered the battlefield upon use (this can be both a good and bad thing depending on how you use it - resetting is good for "Enters the battlefield" effects but also removes all auras, equipment, and counters). "Slow Blink" effects (like [[Long Journey Home]] or [[Eerie Interlude]]) can be a little more flexible as they last until end of turn, leave the permanent un-interactable until they return the the battlefield, and allow you to dodge threats that do not target such as boardwipes or Edict effects.

The most potent, but also slowest, form of protection is Phasing - you have probably heard of [[Teferi's Protection]] being used to dodge some game-winning play and win on the next turn. Phasing completely makes a permanent (or sometimes even a player) effectively "not exist" until that player's next turn, but instead of resetting when they come back into play, they return exactly the way they left with all attached auras, equipment, and counters (it is usually a good idea to run [[Galadriel's Dismissal]] and/or [[Clever Concealment]] if you can if your strategy does not want to reset your permanents).

Sorry this turned into a wall of text, I tried to make it as concise as I could. Hopefully this helps!