In most cases, it is sufficient to know that Thalia, Guardian of Thraben makes non-creature spells cost one more mana. There are a few corner cases where you might need to understand that mechanic at a more in-depth level though. Fundamentally, there are seven steps to casting a spell.
Announce– I’m casting this spell!
Chose modes– For cards like Cryptic Command that have multiple possible modes, make a choice!
Targets– Point your spell at something or someone!
How to divide– If you have a spell that needs to divide something (usually damage), do that now!
Total costs– Determine the actual cost of your spell!
Mana abilities– Tap stuff!
Pay costs– Goodbye, mana!
I remember this with the mnemonic device: All Crazy Teens Have Tried Magic Pills. What?! I’m a teacher and a judge, I eat this kind of stuff up…
Thalia’s ability takes root in the fifth step of casting a spell, the Total Costs portion. To determine the total cost of a spell, you take its base cost (usually a printed number in the upper right corner of the card) and then apply the following in order:
Let’s say there is a Thalia, Guardian of Thraben and a Trinisphere in play. You cast a Swords to Plowshares. The base cost of the card is W. We’ll add in the Thalia tax, bringing the cost to W1. Then we apply Trinisphere, bringing the final cost to W2. Huzzah!
Let’s say your opponent has an Ancestral Vision suspended and you control a Thalia. What happens when that last counter comes off? Looking at the additional rulings makes it very clear:
“If the spell has any mandatory additional costs, you must pay those if able. However, if an additional cost includes a mana payment, you are forced to pay that cost only if there’s enough mana in your mana pool at the time you cast the spell. You aren’t forced to activate any mana abilities, although you may do so if you wish.”
The suspend ability allows you to cast the card without paying its base mana cost. That means that Thalia’s ability still applies, and your opponent will need to pay one if they want to cast their spell. If they do not, Ancestral Vision will just remain in exile with no counters. Neat!
Okay, one more cool one. Let’s say your opponent has an Engineered Explosives and you have a Thalia. Let’s also say that your opponent wants to kill your Thalia with said Engineered Explosives. Your opponent can announce that X will be one. Later in the process of casting the spell, Thalia’s tax comes in and increases the cost by one. Your opponent will now pay two mana for the spell, and if the opponent pays with two different colors of mana, Engineered Explosives will enter with two counters due to Sunburst. Nifty!