When can I special summon, and when can I not?

It's quite simple actually. there are two things you should be aware of when wondering if a monster can be Special Summoned, for exacmple by Monster Reborn, or Call of the Haunted.

1. Card Text: Does the card you want to Summon prevent him from being Special Summoned? here are the three classes of cards we have for this:

Normal: All cards that do not fall within the other two catagories. Example, Vorse Raider.

This wicked Beast-Warrior does every horrid thing imaginable and loves it! His axe bears the marks of his countless victims.

There is nothing in his card text that would prevent him from being Special Summoned.

Semi Nomi: example, is Black Luster Soldier - Envoy of the Beginning.

This card cannot be Normal Summoned or Set. This card can only be Special Summoned by removing from play 1 LIGHT and 1 DARK monster in your Graveyard. Once during each of your turns, you can select and activate 1 of the following effects:
● Select 1 monster on the field, and remove it from play. If you activate this effect, this card cannot attack during this turn.
● If this card destroyed your opponent's monster by battle, it can attack once again in a row.

His effect says "This card can only be Special Summoned by removing from play 1 LIGHT and 1 DARK monster in your Graveyard.". The only-part means that after it was succesfully summoned this way, it can be Special Summoned by other means afterwards. The same rule is applied for regular Synchro, Fusion, Ritual and Xyx Summons.

Nomi: example, Elemental HERO Absolute Zero.

1 "HERO" monster + 1 WATER monster
Must be Fusion Summoned and cannot be Special Summoned by other ways. This card gains 500 ATK for each face-up WATER monster on the field, except "Elemental HERO Absolute Zero". When this card leaves the field: Destroy all monsters your opponent controls.

The card says "Must be Fusion Summoned and cannot be Special Summoned by other ways." This is very simple, and self-explanatory. You cannot Summon it except by Fusion Summon.

2. Only in case of a Semi Nomi card!
For Semi-Nomi cards there is an additional rule. Quite simple, was the card Summoned Succesfully? Most basic example is Stardust Dragon that is summoned by Starlight Road. Starlight Road "Special Summons" Stardust Dragon, which means it was not Synchro Summoned. Therefore, you cannot use Monster Reborn to revive that Stardust Dragon. Another case when a Synchro or Xyz Monster cannot be Special Summoned, is when the initial Summon was negated. Cards that do this are Thunder King Rai-Oh and Solemn Warning. Since they negate the summon, the summon was not succesfull, and hence the monsters cannot be Monster Reborned.

Be aware, this does not count for normal cards. If Obnoxious Celtic Guard were to be Solemn Warninged, you can still use Monster Reborn on it, since the card does not prevent anything from reborning it.