The interaction between Omniscience and Trinisphere
Everything costs three mana or more.

The total cost to cast a spell
= mana cost or alternative cost
+ additional costs and cost increases
- cost reductions


Omniscience provides an alternative cost.
Trinisphere modifies the total cost, the only card to do so.


So start with the alternative cost provided by Omniscience. Then apply any applicable additional costs, cost increases and cost reductions. Then Trinisphere adjusts the total.

For example,


Lightning Bolt would cost {3}.
Cathartic Reunion would cost {3} and Discard two cards.
Apex Hawks kicked twice would cost {W}{W}{2} (since kicking is an additional cost).
Academy Journeymage costs {3} whether you control a Wizard or not.





  117.9. Some spells have alternative costs. An alternative cost is a cost listed in a spell’s text, or applied to it from another effect, that its controller may pay rather than paying the spell’s mana cost. Alternative costs are usually phrased, “You may [action] rather than pay [this object’s] mana cost,” or “You may cast [this object] without paying its mana cost.” Note that some alternative costs are listed in keywords; see rule 702.
  
  601.2f The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect.