Why Tidespout Tyrant?
Tidespout Tyrant became my personal go to after the banning of Paradox Engine due to its small package, powerful synergy, and ability to win almost out of nowhere. In addition to this there is only one card in the package that is bad to draw if you already have the Tyrant (Polymorph). The package is small enough to allow the Urza player to customize the rest of the deck while also having an easy effective combo by playing the cards that you would already want to be playing.
How to Get Tidespout Tyrant
While it is possible to cast the Tidespout Tyrant if drawn off the top of your deck, that is not the primary plan of the deck. Rather you will often use the spells Polymorph or Proteus Staff to kill your own construct token (or Urza in a pinch) and pull the Tyrant out of your deck.
Polymorph: Polymorph is a single target spell that kills your construct or Urza and flips into the next creature off the top of your library. Since there is no creature on your deck excluding the Tyrant the card is guaranteed to flip into the Tyrant. While I find this card to be the weaker of the two polymorph effects, it does come with the benefit of being relatively easy to tutor for due to mystical tutor (and the many effects that find the mystical tutor).
Proteus Staff: The staff is by far the more powerful of the two polymorph effects. Not only are there more ways to tutor for the artifact than there are to find the Polymorph (at least without using tutor chains) you can tutor it directly into play with Whir of Invention at the end of an opponents turn. This card does have the problem of costing two more mana to both cost and activate which could be problematic if you are trying to combo quickly, but that flaw is balanced out by not being a completely dead draw if the Tyrant has been killed, is in your hand, or has been otherwise removed. Due to the wording on Protean Staff, if there are no creatures in your deck you are allowed to stack the deck as you please, often this means you put a big draw spell on top of your deck (such as Windfall) and a two card combo with some disruption to push through your combo (and usually a twister or another way to refill at the end of the cards you draw).
How does Tidespount Tyrant Work?
Tidespout Tyrant is a relatively simple combo, as long as you are able to produce more mana from two artifact cards than the cost of the two cards you can go infinite (and if both are on board you have the ability to bounce one with a card in hand)
Example 1 (With Urza and no artifact that produces more than 1 mana):
Starting hand: You have Tidespout Tyrant, Urza and an untapped Lotus Petal on board and a Pithing Needle in hand. No mana in pool.
Step 1. You tap the Lotus petal to Urza (Producing 1 mana into your mana pool).
Step 2. Cast Pithing Needle (0 mana in pool) triggering the Tidespout Tyrant.
Step 3. Target the Lotus Petal with the bounce ability from Tidespout Tyrant.
Step 4. Lotus Petal is bounced, Pithing needle resolves.
Step 5. Tap Pithing Needle to produce a mana (1 mana in pool).
Step 6. Cast Lotus Petal and trigger the Tidespout Tyrant.
Step 7. Target the Pithing Needle with the bounce ability from Tidespout Tyrant.
Step 8. Pithing Needle is bounced and the Lotus Petal resolves (1 mana still in pool).
Since you started with zero mana and ended up with the same board and hand as you started with you have shown that you can produce a loop with these cards to continue making mana. This will give you an infinite amount of colored mana that you can use into Urza to proceed to get to the win conditions. This cycle works by having at least one zero cost artifact and an artifact that costs no more than 1 mana (You create two mana but have to use one to cast the spell. With two zero cost artifacts you produce two mana).
Example 2 (No Urza, but have artifacts that produce mana).
Starting hand: You have a Tidespout Tyrant and an untapped Mana Vault on Board with a Grafdigger's Cage in hand. No mana in mana pool.
Step 1. Tap the Mana Vault to produce 3 mana (3 mana in pool).
Step 2. Cast Grafdigger's Cage (2 mana in pool) triggering the Tidespout Tyrant.
Step 3. Target the Mana Vault with Tidespout Tyrant's ability.
Step 4. Bounce the Mana Vault and Grafdigger's Cage resolves.
Step 5. Cast Mana Vault (1 mana in pool) triggering the Tidespout Tyrant.
Step 6. Target the Grafdigger's Cage with the Tidespout Tyrant's ability.
Step 7. Grafdigger's Cage is Bounced and the Mana Vault resolves (1 mana in pool).
At the end of the example you have demonstrated a loop where you are able to gain a single mana per iteration, giving you infinite colorless mana. Providing you are able to cast Urza you are able to win the game from this point (and if you have another mana rock that can produce a colored mana you can make infinite mana then start bouncing the colored mana rock and the Vault to produce the necessary colored mana). You can also do this combo with a Sol Ring/Mana Crypt and a zero mana artifact, or a Grim Monolith and a zero mana artifact (or the Sol Ring with the Mana Crypt or Grim Monolith). Providing the net gain of the loop exceeds the net loss you will produce infinite mana.